diff --git a/qiskit/quantum_info/synthesis/two_qubit_decompose.py b/qiskit/quantum_info/synthesis/two_qubit_decompose.py
index b15e25a476eb..b0407961f768 100644
--- a/qiskit/quantum_info/synthesis/two_qubit_decompose.py
+++ b/qiskit/quantum_info/synthesis/two_qubit_decompose.py
@@ -382,7 +382,7 @@ def traces(self, target):
                 4]
 
     @staticmethod
-    def decomp0(target):
+    def decomp0(target, eps=1e-15):
         """Decompose target ~Ud(x, y, z) with 0 uses of the basis gate.
         Result Ur has trace:
         :math:`|Tr(Ur.Utarget^dag)| = 4|(cos(x)cos(y)cos(z)+ j sin(x)sin(y)sin(z)|`,
@@ -390,7 +390,10 @@ def decomp0(target):
 
         U0l = target.K1l.dot(target.K2l)
         U0r = target.K1r.dot(target.K2r)
-
+        U0l.real[abs(U0l.real) < eps] = 0.0
+        U0l.imag[abs(U0l.imag) < eps] = 0.0
+        U0r.real[abs(U0r.real) < eps] = 0.0
+        U0r.imag[abs(U0r.imag) < eps] = 0.0
         return U0r, U0l
 
     def decomp1(self, target):