diff --git a/sklearn/covariance/tests/test_graphical_lasso.py b/sklearn/covariance/tests/test_graphical_lasso.py
index 317bf2aa85124..aaee1919e8dcc 100644
--- a/sklearn/covariance/tests/test_graphical_lasso.py
+++ b/sklearn/covariance/tests/test_graphical_lasso.py
@@ -24,7 +24,12 @@
 )
 
 
-def test_graphical_lasso(random_state=0):
+def test_graphical_lassos(random_state=1):
+    """Test the graphical lasso solvers.
+
+    This checks is unstable for some random seeds where the covariance found with "cd"
+    and "lars" solvers are different (4 cases / 100 tries).
+    """
     # Sample data from a sparse multivariate normal
     dim = 20
     n_samples = 100
@@ -46,10 +51,11 @@ def test_graphical_lasso(random_state=0):
             costs, dual_gap = np.array(costs).T
             # Check that the costs always decrease (doesn't hold if alpha == 0)
             if not alpha == 0:
-                assert_array_less(np.diff(costs), 0)
+                # use 1e-12 since the cost can be exactly 0
+                assert_array_less(np.diff(costs), 1e-12)
         # Check that the 2 approaches give similar results
-        assert_array_almost_equal(covs["cd"], covs["lars"], decimal=4)
-        assert_array_almost_equal(icovs["cd"], icovs["lars"], decimal=4)
+        assert_allclose(covs["cd"], covs["lars"], atol=1e-4)
+        assert_allclose(icovs["cd"], icovs["lars"], atol=1e-4)
 
     # Smoke test the estimator
     model = GraphicalLasso(alpha=0.25).fit(X)