diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 492ca8d2d..4b03e8f56 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -105,8 +105,10 @@ class Rotation:
             Rotation to check for equality.
 
         """
+        ambiguous = np.isclose(self.quaternion[...,0],0)
         return      np.prod(self.shape,dtype=int) == np.prod(other.shape,dtype=int) \
-                and np.allclose(self.quaternion,other.quaternion)
+                and (   np.allclose(self.quaternion,other.quaternion) \
+                     or np.allclose(self.quaternion[ambiguous],-1*other.quaternion[ambiguous]))
 
 
     @property
diff --git a/python/tests/test_Rotation.py b/python/tests/test_Rotation.py
index f8f1a3da7..bc6614fb9 100644
--- a/python/tests/test_Rotation.py
+++ b/python/tests/test_Rotation.py
@@ -786,6 +786,12 @@ class TestRotation:
     def test_equal(self):
         assert Rotation.from_random(rng_seed=1) == Rotation.from_random(rng_seed=1)
 
+    def test_equal_ambiguous(self):
+        qu = np.random.rand(10,4)
+        qu[:,0] = 0.
+        qu/=np.linalg.norm(qu,axis=1,keepdims=True)
+        assert Rotation(qu) == Rotation(-qu)
+
     def test_inversion(self):
         r = Rotation.from_random()
         assert r == ~~r