diff --git a/src/iso19111/io.cpp b/src/iso19111/io.cpp
index b73543e1c8..f693c4985b 100644
--- a/src/iso19111/io.cpp
+++ b/src/iso19111/io.cpp
@@ -9495,7 +9495,6 @@ const std::string &PROJStringFormatter::toString() const {
             }
 
             if (curStep.name == "helmert" && prevStep.name == "helmert" &&
-                !curStep.inverted && !prevStep.inverted &&
                 curStepParamCount == 3 &&
                 curStepParamCount == prevStepParamCount) {
                 std::map<std::string, double> leftParamsMap;
@@ -9520,12 +9519,18 @@ const std::string &PROJStringFormatter::toString() const {
                     rightParamsMap.find(y) != rightParamsMap.end() &&
                     rightParamsMap.find(z) != rightParamsMap.end()) {
 
-                    const double xSum = leftParamsMap[x] + rightParamsMap[x];
-                    const double ySum = leftParamsMap[y] + rightParamsMap[y];
-                    const double zSum = leftParamsMap[z] + rightParamsMap[z];
+                    const double signLeft = prevStep.inverted ? -1 : 1;
+                    const double signRight = curStep.inverted ? -1 : 1;
+                    const double xSum = signLeft * leftParamsMap[x] +
+                                        signRight * rightParamsMap[x];
+                    const double ySum = signLeft * leftParamsMap[y] +
+                                        signRight * rightParamsMap[y];
+                    const double zSum = signLeft * leftParamsMap[z] +
+                                        signRight * rightParamsMap[z];
                     if (xSum == 0.0 && ySum == 0.0 && zSum == 0.0) {
                         deletePrevAndCurIter();
                     } else {
+                        prevStep.inverted = false;
                         prevStep.paramValues[0] =
                             Step::KeyValue("x", internal::toString(xSum));
                         prevStep.paramValues[1] =
@@ -9542,7 +9547,7 @@ const std::string &PROJStringFormatter::toString() const {
 
             // Helmert followed by its inverse is a no-op
             if (curStep.name == "helmert" && prevStep.name == "helmert" &&
-                !curStep.inverted && !prevStep.inverted &&
+                (curStep.inverted == prevStep.inverted) &&
                 curStepParamCount == prevStepParamCount) {
                 std::set<std::string> leftParamsSet;
                 std::set<std::string> rightParamsSet;
diff --git a/test/unit/test_io.cpp b/test/unit/test_io.cpp
index ab239dbaaf..0eaf68cf0d 100644
--- a/test/unit/test_io.cpp
+++ b/test/unit/test_io.cpp
@@ -10201,31 +10201,137 @@ TEST(io, projstringformatter_helmert_7_param_noop) {
 // ---------------------------------------------------------------------------
 
 TEST(io, projstringformatter_merge_consecutive_helmert_3_param) {
-    auto fmt = PROJStringFormatter::create();
-    fmt->addStep("helmert");
-    fmt->addParam("x", 10);
-    fmt->addParam("y", 20);
-    fmt->addParam("z", 30);
-    fmt->addStep("helmert");
-    fmt->addParam("x", -1);
-    fmt->addParam("y", -2);
-    fmt->addParam("z", -3);
-    EXPECT_EQ(fmt->toString(), "+proj=helmert +x=9 +y=18 +z=27");
+    {
+        auto fmt = PROJStringFormatter::create();
+        fmt->addStep("helmert");
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+
+        fmt->addStep("helmert");
+        fmt->addParam("x", -1);
+        fmt->addParam("y", -2);
+        fmt->addParam("z", -3);
+        EXPECT_EQ(fmt->toString(), "+proj=helmert +x=9 +y=18 +z=27");
+    }
+
+    {
+        auto fmt = PROJStringFormatter::create();
+        fmt->addStep("helmert");
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+
+        fmt->addStep("helmert");
+        fmt->setCurrentStepInverted(true);
+        fmt->addParam("x", -10);
+        fmt->addParam("y", -20);
+        fmt->addParam("z", -30);
+        EXPECT_EQ(fmt->toString(), "+proj=helmert +x=20 +y=40 +z=60");
+    }
+
+    {
+        auto fmt = PROJStringFormatter::create();
+        fmt->addStep("helmert");
+        fmt->setCurrentStepInverted(true);
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+
+        fmt->addStep("helmert");
+        fmt->addParam("x", -10);
+        fmt->addParam("y", -20);
+        fmt->addParam("z", -30);
+        EXPECT_EQ(fmt->toString(), "+proj=helmert +x=-20 +y=-40 +z=-60");
+    }
 }
 
 // ---------------------------------------------------------------------------
 
 TEST(io, projstringformatter_merge_consecutive_helmert_3_param_noop) {
-    auto fmt = PROJStringFormatter::create();
-    fmt->addStep("helmert");
-    fmt->addParam("x", 10);
-    fmt->addParam("y", 20);
-    fmt->addParam("z", 30);
-    fmt->addStep("helmert");
-    fmt->addParam("x", -10);
-    fmt->addParam("y", -20);
-    fmt->addParam("z", -30);
-    EXPECT_EQ(fmt->toString(), "+proj=noop");
+    {
+        auto fmt = PROJStringFormatter::create();
+        fmt->addStep("helmert");
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+
+        fmt->addStep("helmert");
+        fmt->addParam("x", -10);
+        fmt->addParam("y", -20);
+        fmt->addParam("z", -30);
+        EXPECT_EQ(fmt->toString(), "+proj=noop");
+    }
+
+    {
+        auto fmt = PROJStringFormatter::create();
+        fmt->addStep("helmert");
+        fmt->setCurrentStepInverted(true);
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+
+        fmt->addStep("helmert");
+        fmt->setCurrentStepInverted(true);
+        fmt->addParam("x", -10);
+        fmt->addParam("y", -20);
+        fmt->addParam("z", -30);
+        EXPECT_EQ(fmt->toString(), "+proj=noop");
+    }
+}
+
+// ---------------------------------------------------------------------------
+
+TEST(io, projstringformatter_merge_consecutive_helmert_7_param_noop) {
+    {
+        auto fmt = PROJStringFormatter::create();
+        fmt->addStep("helmert");
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+        fmt->addParam("rx", 1);
+        fmt->addParam("ry", 2);
+        fmt->addParam("rz", 3);
+        fmt->addParam("s", 4);
+        fmt->addParam("convention", "position_vector");
+
+        fmt->addStep("helmert");
+        fmt->addParam("x", -10);
+        fmt->addParam("y", -20);
+        fmt->addParam("z", -30);
+        fmt->addParam("rx", -1);
+        fmt->addParam("ry", -2);
+        fmt->addParam("rz", -3);
+        fmt->addParam("s", -4);
+        fmt->addParam("convention", "position_vector");
+        EXPECT_EQ(fmt->toString(), "+proj=noop");
+    }
+
+    {
+        auto fmt = PROJStringFormatter::create();
+        fmt->addStep("helmert");
+        fmt->setCurrentStepInverted(true);
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+        fmt->addParam("rx", 1);
+        fmt->addParam("ry", 2);
+        fmt->addParam("rz", 3);
+        fmt->addParam("s", 4);
+        fmt->addParam("convention", "position_vector");
+
+        fmt->addStep("helmert");
+        fmt->setCurrentStepInverted(true);
+        fmt->addParam("x", -10);
+        fmt->addParam("y", -20);
+        fmt->addParam("z", -30);
+        fmt->addParam("rx", -1);
+        fmt->addParam("ry", -2);
+        fmt->addParam("rz", -3);
+        fmt->addParam("s", -4);
+        fmt->addParam("convention", "position_vector");
+        EXPECT_EQ(fmt->toString(), "+proj=noop");
+    }
 }
 
 // ---------------------------------------------------------------------------
@@ -10242,11 +10348,37 @@ TEST(io, projstringformatter_merge_inverted_helmert_with_opposite_conventions) {
         fmt->addParam("rz", 3);
         fmt->addParam("s", 4);
         fmt->addParam("convention", "position_vector");
+
+        fmt->addStep("helmert");
+        fmt->setCurrentStepInverted(true);
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
+        fmt->addParam("rx", -1);
+        fmt->addParam("ry", -2);
+        fmt->addParam("rz", -3);
+        fmt->addParam("s", 4);
+        fmt->addParam("convention", "coordinate_frame");
+        EXPECT_EQ(fmt->toString(), "+proj=noop");
+    }
+
+    {
+        auto fmt = PROJStringFormatter::create();
         fmt->addStep("helmert");
         fmt->setCurrentStepInverted(true);
         fmt->addParam("x", 10);
         fmt->addParam("y", 20);
         fmt->addParam("z", 30);
+        fmt->addParam("rx", 1);
+        fmt->addParam("ry", 2);
+        fmt->addParam("rz", 3);
+        fmt->addParam("s", 4);
+        fmt->addParam("convention", "position_vector");
+
+        fmt->addStep("helmert");
+        fmt->addParam("x", 10);
+        fmt->addParam("y", 20);
+        fmt->addParam("z", 30);
         fmt->addParam("rx", -1);
         fmt->addParam("ry", -2);
         fmt->addParam("rz", -3);
@@ -10267,6 +10399,7 @@ TEST(io, projstringformatter_merge_inverted_helmert_with_opposite_conventions) {
         fmt->addParam("rz", 3);
         fmt->addParam("s", 4);
         fmt->addParam("convention", "coordinate_frame");
+
         fmt->addStep("helmert");
         fmt->addParam("x", 10);
         fmt->addParam("y", 20);
@@ -10291,6 +10424,7 @@ TEST(io, projstringformatter_merge_inverted_helmert_with_opposite_conventions) {
         fmt->addParam("rz", 3);
         fmt->addParam("s", 4);
         fmt->addParam("convention", "position_vector");
+
         fmt->addStep("helmert");
         // fmt->setCurrentStepInverted(true); <== CAUSE
         fmt->addParam("x", 10);
@@ -10316,6 +10450,7 @@ TEST(io, projstringformatter_merge_inverted_helmert_with_opposite_conventions) {
         fmt->addParam("rz", 3);
         fmt->addParam("s", 4);
         fmt->addParam("convention", "position_vector");
+
         fmt->addStep("helmert");
         fmt->setCurrentStepInverted(true);
         fmt->addParam("x", 10);
@@ -10341,6 +10476,7 @@ TEST(io, projstringformatter_merge_inverted_helmert_with_opposite_conventions) {
         fmt->addParam("rz", 3);
         fmt->addParam("s", 4);
         fmt->addParam("convention", "position_vector");
+
         fmt->addStep("helmert");
         fmt->setCurrentStepInverted(true);
         fmt->addParam("x", -10); // <== CAUSE
@@ -10366,6 +10502,7 @@ TEST(io, projstringformatter_merge_inverted_helmert_with_opposite_conventions) {
         fmt->addParam("rz", 2);
         fmt->addParam("s", 4);
         fmt->addParam("convention", "position_vector");
+
         fmt->addStep("helmert");
         fmt->setCurrentStepInverted(true);
         fmt->addParam("x", 10);