diff --git a/spatialmath/base/transformsNd.py b/spatialmath/base/transformsNd.py
index 57476d05..c04e5d8b 100644
--- a/spatialmath/base/transformsNd.py
+++ b/spatialmath/base/transformsNd.py
@@ -380,7 +380,7 @@ def isR(R: NDArray, tol: float = 20) -> bool:  # -> TypeGuard[SOnArray]:
     """
     return bool(
         np.linalg.norm(R @ R.T - np.eye(R.shape[0])) < tol * _eps
-        and np.linalg.det(R @ R.T) > 0
+        and np.linalg.det(R) > 0
     )
 
 
diff --git a/tests/base/test_transforms3d.py b/tests/base/test_transforms3d.py
index f7eb5248..2f1e6049 100755
--- a/tests/base/test_transforms3d.py
+++ b/tests/base/test_transforms3d.py
@@ -61,6 +61,14 @@ def test_checks(self):
         nt.assert_equal(isrot(T, True), False)
         nt.assert_equal(ishom(T, True), False)
 
+        # reflection case
+        T = np.array([[-1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        nt.assert_equal(isR(T), False)
+        nt.assert_equal(isrot(T), True)
+        nt.assert_equal(ishom(T), False)
+        nt.assert_equal(isrot(T, True), False)
+        nt.assert_equal(ishom(T, True), False)
+
     def test_trinv(self):
         T = np.eye(4)
         nt.assert_array_almost_equal(trinv(T), T)