diff --git a/qiskit_algorithms/optimizers/spsa.py b/qiskit_algorithms/optimizers/spsa.py
index 707409ef..10d81dfd 100644
--- a/qiskit_algorithms/optimizers/spsa.py
+++ b/qiskit_algorithms/optimizers/spsa.py
@@ -727,7 +727,7 @@ def _batch_evaluate(function, points, max_evals_grouped):
         num_batches += 1
 
     # split the points
-    batched_points = np.split(np.asarray(points), num_batches)
+    batched_points = np.array_split(np.asarray(points), num_batches)
 
     results = []
     for batch in batched_points:
diff --git a/test/optimizers/test_spsa.py b/test/optimizers/test_spsa.py
index 55e4b7b3..5f31d69d 100644
--- a/test/optimizers/test_spsa.py
+++ b/test/optimizers/test_spsa.py
@@ -181,3 +181,17 @@ def callback(nfev, point, fval, update, accepted):
         for i, (key, values) in enumerate(history.items()):
             self.assertTrue(all(isinstance(value, expected_types[i]) for value in values))
             self.assertEqual(len(history[key]), maxiter)
+
+    @data(1, 2, 3, 4)
+    def test_estimate_stddev(self, max_evals_grouped):
+        """Test the estimate_stddev
+        See https://github.com/Qiskit/qiskit-nature/issues/797"""
+
+        def objective(x):
+            if len(x.shape) == 2:
+                return np.array([sum(x_i) for x_i in x])
+            return sum(x)
+
+        point = np.ones(5)
+        result = SPSA.estimate_stddev(objective, point, avg=10, max_evals_grouped=max_evals_grouped)
+        self.assertAlmostEqual(result, 0)