diff --git a/tests/testPreconditioner.cpp b/tests/testPreconditioner.cpp
index 40d49a934..46b243913 100644
--- a/tests/testPreconditioner.cpp
+++ b/tests/testPreconditioner.cpp
@@ -42,6 +42,21 @@ static GaussianFactorGraph createSimpleGaussianFactorGraph() {
   return fg;
 }
 
+/* ************************************************************************* */
+static GaussianFactorGraph createSimpleGaussianFactorGraphUnordered() {
+  GaussianFactorGraph fg;
+  SharedDiagonal unit2 = noiseModel::Unit::Create(2);
+  // linearized prior on x1: c[_x1_]+x1=0 i.e. x1=-c[_x1_
+  fg += JacobianFactor(2, 10*eye(2), -1.0*ones(2), unit2);
+  // odometry between x1 and x2: x2-x1=[0.2;-0.1]
+  fg += JacobianFactor(2, -10*eye(2), 1, 10*eye(2), (Vector(2) << 2.0, -1.0), unit2);
+  // measurement between x1 and l1: l1-x1=[0.0;0.2]
+  fg += JacobianFactor(2, -5*eye(2), 1, 5*eye(2), (Vector(2) << 0.0, 1.0), unit2);
+  // measurement between x2 and l1: l1-x2=[-0.2;0.3]
+  fg += JacobianFactor(0, -5*eye(2), 1, 5*eye(2), (Vector(2) << -1.0, 1.5), unit2);
+  return fg;
+}
+
 /* ************************************************************************* */
 // Copy of BlockJacobiPreconditioner::build
 std::vector<Matrix> buildBlocks( const GaussianFactorGraph &gfg, const KeyInfo &keyInfo)
@@ -89,10 +104,6 @@ std::vector<Matrix> buildBlocks( const GaussianFactorGraph &gfg, const KeyInfo &
 TEST( Preconditioner, buildBlocks ) {
   // Create simple Gaussian factor graph and initial values
   GaussianFactorGraph gfg = createSimpleGaussianFactorGraph();
-  Values initial;
-  initial.insert(0,Point2(4, 5));
-  initial.insert(1,Point2(0,  1));
-  initial.insert(2,Point2(-5, 7));
 
   // Expected Hessian block diagonal matrices
   std::map<Key, Matrix> expectedHessian =gfg.hessianBlockDiagonal();
@@ -110,6 +121,28 @@ TEST( Preconditioner, buildBlocks ) {
     EXPECT(assert_equal(it1->second, *it2));
 }
 
+/* ************************************************************************* */
+TEST( Preconditioner, buildBlocks2 ) {
+  // Create simple Gaussian factor graph and initial values
+  GaussianFactorGraph gfg = createSimpleGaussianFactorGraphUnordered();
+
+  // Expected Hessian block diagonal matrices
+  std::map<Key, Matrix> expectedHessian =gfg.hessianBlockDiagonal();
+
+  // Actual Hessian block diagonal matrices from BlockJacobiPreconditioner::build
+  std::vector<Matrix> actualHessian = buildBlocks(gfg, KeyInfo(gfg));
+
+  // Compare the number of block diagonal matrices
+  EXPECT_LONGS_EQUAL(expectedHessian.size(), 3);
+  EXPECT_LONGS_EQUAL(expectedHessian.size(), actualHessian.size());
+
+  // Compare the values of matrices
+  std::map<Key, Matrix>::const_iterator it1 = expectedHessian.begin();
+  std::vector<Matrix>::const_iterator it2 = actualHessian.begin();
+  for(; it1!=expectedHessian.end(); it1++, it2++)
+    EXPECT(assert_equal(it1->second, *it2));
+}
+
 /* ************************************************************************* */
 int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
 /* ************************************************************************* */