diff --git a/strawberryfields/utils/random_numbers_matrices.py b/strawberryfields/utils/random_numbers_matrices.py
index 5062f2780..6b37f07af 100644
--- a/strawberryfields/utils/random_numbers_matrices.py
+++ b/strawberryfields/utils/random_numbers_matrices.py
@@ -110,12 +110,10 @@ def random_interferometer(N, real=False):
     Returns:
         array: random :math:`N\times N` unitary distributed with the Haar measure
     """
+    if N == 1:
+        if real:
+            return np.array([[2 * (np.random.binomial(1, 0.5) - 0.5)]])
+        return np.array([[np.exp(1j * 2 * np.pi * np.random.rand())]])
     if real:
-        z = np.random.randn(N, N)
-    else:
-        z = randnc(N, N) / np.sqrt(2.0)
-    q, r = sp.linalg.qr(z)
-    d = np.diagonal(r)
-    ph = d / np.abs(d)
-    U = np.multiply(q, ph, q)
-    return U
+        return sp.stats.ortho_group.rvs(N)
+    return sp.stats.unitary_group.rvs(N)
diff --git a/tests/frontend/test_utils.py b/tests/frontend/test_utils.py
index 05562f02c..06c0dd575 100644
--- a/tests/frontend/test_utils.py
+++ b/tests/frontend/test_utils.py
@@ -267,14 +267,10 @@ def test_odd_cat_state(self, a, cutoff, tol):
 # ===================================================================================
 
 
+@pytest.mark.parametrize("modes", [1, 2, 3])
 class TestRandomMatrices:
     """Unit tests for random matrices"""
 
-    @pytest.fixture
-    def modes(self):
-        """Number of modes to use when creating matrices"""
-        return 3
-
     @pytest.mark.parametrize("pure_state", [True, False])
     @pytest.mark.parametrize("block_diag", [True, False])
     def test_random_covariance_square(self, modes, hbar, pure_state, block_diag):