diff --git a/cpmpy/expressions/globalconstraints.py b/cpmpy/expressions/globalconstraints.py
index 4dd300e33..9fffbc5b6 100644
--- a/cpmpy/expressions/globalconstraints.py
+++ b/cpmpy/expressions/globalconstraints.py
@@ -237,15 +237,21 @@ def decompose(self):
         """
         succ = cpm_array(self.args)
         n = len(succ)
-        order = intvar(0,n-1, shape=n)
+        order = intvar(0,n-1, shape=n, name='order')
         constraining = []
         constraining += [AllDifferent(succ)] # different successors
         constraining += [AllDifferent(order)] # different orders
         constraining += [order[n-1] == 0] # symmetry breaking, last one is '0'
-
-        defining = [order[0] == succ[0]]
-        defining += [order[i] == succ[order[i-1]] for i in range(1,n)] # first one is successor of '0', ith one is successor of i-1
-
+        a = boolvar(name='a')
+
+        defining = [a == ((Minimum(succ) >= 0) & (Maximum(succ) < n))]
+        for i in range(n):
+            defining += [(~a).implies(order[i] == 0)] #make order be totally defined
+            if i == 0:
+                defining += [a.implies(order[0] == succ[0])]
+            else:
+                defining += [a.implies(
+                    order[i] == succ[order[i - 1]])]  # first one is successor of '0', ith one is successor of i-1
         return constraining, defining
 
     def value(self):
diff --git a/tests/test_globalconstraints.py b/tests/test_globalconstraints.py
index a4c3db386..49c444fa3 100644
--- a/tests/test_globalconstraints.py
+++ b/tests/test_globalconstraints.py
@@ -123,10 +123,10 @@ def test_circuit(self):
         self.assertTrue(cp.Circuit(x).value())
 
     def test_not_circuit(self):
-        x = cp.intvar(lb=0, ub=2, shape=3)
+        x = cp.intvar(lb=-1, ub=5, shape=4)
         circuit = cp.Circuit(x)
 
-        model = cp.Model([~circuit, x == [1,2,0]])
+        model = cp.Model([~circuit, x == [1,2,3,0]])
         self.assertFalse(model.solve())
 
         model = cp.Model([~circuit])