diff --git a/Orange/preprocess/preprocess.py b/Orange/preprocess/preprocess.py
index 8a98b683369..a272739c751 100644
--- a/Orange/preprocess/preprocess.py
+++ b/Orange/preprocess/preprocess.py
@@ -190,8 +190,8 @@ def __call__(self, data):
         data : an input dataset
         """
 
-        oks = bn.nanmin(data.X, axis=0) != \
-              bn.nanmax(data.X, axis=0)
+        oks = np.logical_and(~bn.allnan(data.X, axis=0),
+                             bn.nanmin(data.X, axis=0) != bn.nanmax(data.X, axis=0))
         atts = [data.domain.attributes[i] for i, ok in enumerate(oks) if ok]
         domain = Orange.data.Domain(atts, data.domain.class_vars,
                                     data.domain.metas)
diff --git a/Orange/tests/test_preprocess.py b/Orange/tests/test_preprocess.py
index dcda85c77cd..c4072dde259 100644
--- a/Orange/tests/test_preprocess.py
+++ b/Orange/tests/test_preprocess.py
@@ -61,10 +61,11 @@ def test_refuse_data_in_constructor(self):
 
 class TestRemoveConstant(unittest.TestCase):
     def test_remove_columns(self):
-        X = np.random.rand(6, 4)
+        X = np.random.rand(6, 5)
         X[:, (1,3)] = 5
         X[3, 1] = np.nan
         X[1, 1] = np.nan
+        X[:, 4] = np.nan
         data = Table(X)
         d = RemoveConstant()(data)
         self.assertEqual(len(d.domain.attributes), 2)