diff --git a/test/unit/test_matrices.py b/test/unit/test_matrices.py
index 306637ee7..4f8ab1d1e 100644
--- a/test/unit/test_matrices.py
+++ b/test/unit/test_matrices.py
@@ -39,6 +39,7 @@
 from pyop2 import op2
 from pyop2.exceptions import MapValueError, ModeValueError
 from pyop2.mpi import COMM_WORLD
+from pyop2.datatypes import IntType
 
 from petsc4py.PETSc import ScalarType
 
@@ -941,6 +942,45 @@ def test_assemble_mixed_rhs_vector(self, mset, mmap, mvdat):
         assert_allclose(dat[1].data_ro, exp, eps)
 
 
+def test_matrices_sparsity_blockwise_specification():
+    #
+    # 0    1    2    3   nodesetA
+    # x----x----x----x
+    #   0     1    2     setA
+    #
+    #      0    1    2   nodesetB
+    #      x----x----x
+    #         0    1     setB
+    #
+    #   0 1 2 3 | 0 1 2
+    # 0 x       |
+    # 1   x     | x x
+    # 2     x   | x x x
+    # 3       x |   x x  sparsity
+    # ----------+------
+    # 0   x x   | x
+    # 1   x x x |   x
+    # 2     x x |     x
+    #
+    arity = 2
+    setA = op2.Set(3)
+    nodesetA = op2.Set(4)
+    setB = op2.Set(2)
+    nodesetB = op2.Set(3)
+    nodesetAB = op2.MixedSet((nodesetA, nodesetB))
+    datasetAB = nodesetAB ** 1
+    mapA = op2.Map(setA, nodesetA, arity, values=[[0, 1], [1, 2], [2, 3]])
+    mapB = op2.Map(setB, nodesetB, arity, values=[[0, 1], [1, 2]])
+    mapBA = op2.Map(setB, setA, 1, values=[1, 2])
+    mapAB = op2.Map(setA, setB, 1, values=[-1, 0, 1])  # "inverse" map
+    s = op2.Sparsity((datasetAB, datasetAB), {(1, 0): [(mapB, op2.ComposedMap(mapA, mapBA), None)],
+                                              (0, 1): [(mapA, op2.ComposedMap(mapB, mapAB), None)]})
+    assert np.all(s._blocks[0][0].nnz == np.array([1, 1, 1, 1], dtype=IntType))
+    assert np.all(s._blocks[0][1].nnz == np.array([0, 2, 3, 2], dtype=IntType))
+    assert np.all(s._blocks[1][0].nnz == np.array([2, 3, 2], dtype=IntType))
+    assert np.all(s._blocks[1][1].nnz == np.array([1, 1, 1], dtype=IntType))
+
+
 if __name__ == '__main__':
     import os
     pytest.main(os.path.abspath(__file__))