diff --git a/nibabel/tests/test_nifti1.py b/nibabel/tests/test_nifti1.py
index 6aab35aff0..065ac1d404 100644
--- a/nibabel/tests/test_nifti1.py
+++ b/nibabel/tests/test_nifti1.py
@@ -357,7 +357,9 @@ def test_qform_sform(self):
         another_aff = np.diag([3, 4, 5, 1])
         # Affine with shears
         nasty_aff = from_matvec(np.arange(9).reshape((3, 3)), [9, 10, 11])
+        nasty_aff[0, 0] = 1  # Make full rank
         fixed_aff = unshear_44(nasty_aff)
+        assert_false(np.allclose(fixed_aff, nasty_aff))
         for in_meth, out_meth in ((hdr.set_qform, hdr.get_qform),
                                   (hdr.set_sform, hdr.get_sform)):
             in_meth(nice_aff, 2)