diff --git a/scipy/spatial/transform/rotation.pyx b/scipy/spatial/transform/rotation.pyx
index fe640762f396..0af9a1ae1765 100644
--- a/scipy/spatial/transform/rotation.pyx
+++ b/scipy/spatial/transform/rotation.pyx
@@ -176,7 +176,7 @@ cdef double[:, :] _compute_euler_from_matrix(
                 _angles[2] = -atan2(matrix_trans[1, 0] + matrix_trans[0, 1],
                                     matrix_trans[0, 0] - matrix_trans[1, 1])
         else:
-            # For instrinsic, set third angle to zero
+            # For intrinsic, set third angle to zero
             # 6a
             if not safe:
                 _angles[2] = 0
@@ -209,16 +209,16 @@ cdef double[:, :] _compute_euler_from_matrix(
             elif _angles[i] > pi:
                 _angles[i] -= 2 * pi
 
+        if extrinsic:
+            # reversal
+            _angles[0], _angles[2] = _angles[2], _angles[0]
+
         # Step 8
         if not safe:
             warnings.warn("Gimbal lock detected. Setting third angle to zero "
                           "since it is not possible to uniquely determine "
                           "all angles.")
 
-    # Reverse role of extrinsic and intrinsic rotations, but let third angle be
-    # zero for gimbal locked cases. Take a copy, to enforce contiguous memory layout.
-    if extrinsic:
-        angles = angles[:, ::-1].copy()
     return angles
 
 @cython.boundscheck(False)