diff --git a/datastock/_generic_check.py b/datastock/_generic_check.py
index 035da81..975e61b 100644
--- a/datastock/_generic_check.py
+++ b/datastock/_generic_check.py
@@ -420,7 +420,20 @@ def _check_vectbasis(
     e2=None,
     dim=None,
     tol=None,
+    direct=None,
 ):
+    """ Check a 2d or 3d set of unit vectors
+
+    Check that:
+        - vectors are defined (if None, they can be inferred)
+
+    Normalizes vectorto be unit vectors
+    Optionally (default) check the vectors forma direct basis
+    """
+
+    # ----------------
+    # check inputs
+    # ----------------
 
     # dim
     dim = _check_var(dim, 'dim', types=int, default=3, allowed=[2, 3])
@@ -428,6 +441,13 @@ def _check_vectbasis(
     # tol
     tol = _check_var(tol, 'tol', types=float, default=1.e-14, sign='>0.')
 
+    # direct
+    direct = _check_var(direct, 'direct', types=bool, default=True)
+
+    # ----------------------
+    # check what's provided
+    # ----------------------
+
     # check is provided
     if e0 is not None:
         e0 = _check_flat1darray(e0, 'e0', size=dim, dtype=float, norm=True)
@@ -436,13 +456,23 @@ def _check_vectbasis(
     if e2 is not None:
         e2 = _check_flat1darray(e2, 'e2', size=dim, dtype=float, norm=True)
 
+    # preliminary
+    allnone = all([ee is None for ee in [e0, e1, e2][:dim]])
+    if allnone is True:
+        lstr = [f"\t- {ee}" for ee in ['e0', 'e1', 'e2'][:dim]]
+        msg = (
+            f"For a basis f dimension {dim}, provide at least one of:\n"
+            + "\n".join(lstr)
+        )
+        raise Exception(msg)
+
+    # ----------------------
+    # dim = 2
+    # ----------------------
+
     # vectors
     if dim == 2:
 
-        if e0 is None and e1 is None:
-            msg = "Please provide e0 and/or e1!"
-            raise Exception(msg)
-
         # complete if missing
         if e0 is None:
             e0 = np.r_[e1[1], -e1[0]]
@@ -455,16 +485,18 @@ def _check_vectbasis(
             raise Exception(msg)
 
         # direct
-        if np.abs(np.cross(e0, e1).tolist() - 1.) < tol:
-            msg = "Non-direct basis"
-            raise Exception(msg)
+        if direct is True:
+            if np.abs(np.cross(e0, e1).tolist() - 1.) < tol:
+                msg = "Non-direct basis"
+                raise Exception(msg)
 
         return e0, e1
 
+    # ----------------------
+    # dim = 3
+    # ----------------------
+
     else:
-        if e0 is None and e1 is None and e2 is None:
-            msg = "Please provide at least e0, e1 or e2!"
-            raise Exception(msg)
 
         # complete if 2 missing
         if e0 is None and e1 is None:
@@ -472,7 +504,7 @@ def _check_vectbasis(
         elif e0 is None and e2 is None:
             e2 = _get_vertical_unitvect(ee=e1)
         elif e1 is None and e2 is None:
-            e2 = _get_vertical_unitvect(ee=e0)
+            e2 = _get_horizontal_unitvect(ee=e0)
 
         # complete if 1 missing
         if e0 is None:
@@ -502,9 +534,10 @@ def _check_vectbasis(
             raise Exception(msg)
 
         # direct
-        if not np.allclose(np.cross(e0, e1), e2, atol=tol, rtol=1e-6):
-            msg = "Non-direct basis"
-            raise Exception(msg)
+        if direct is True:
+            if not np.allclose(np.cross(e0, e1), e2, atol=tol, rtol=1e-6):
+                msg = "Non-direct basis"
+                raise Exception(msg)
 
         return e0, e1, e2