diff --git a/qiskit/circuit/library/standard_gates/equivalence_library.py b/qiskit/circuit/library/standard_gates/equivalence_library.py
index 51f1688a0e7e..88afa3e54dac 100644
--- a/qiskit/circuit/library/standard_gates/equivalence_library.py
+++ b/qiskit/circuit/library/standard_gates/equivalence_library.py
@@ -869,29 +869,16 @@ def _cnot_rxx_decompose(plus_ry: bool = True, plus_rxx: bool = True):
 # «     └──────────┘                 └──────┘└─────────┘ └────┘└──────────┘
 #
 q = QuantumRegister(2, "q")
-def_swap_ecr = QuantumCircuit(q, global_phase=pi / 2)
-def_swap_ecr.rz(pi / 2, 0)
-def_swap_ecr.sx(0)
-def_swap_ecr.rz(pi / 2, 1)
-def_swap_ecr.sx(1)
-def_swap_ecr.rz(-pi, 1)
-def_swap_ecr.ecr(0, 1)
-def_swap_ecr.rz(pi / 2, 1)
-def_swap_ecr.sx(1)
-def_swap_ecr.rz(pi / 2, 0)
-def_swap_ecr.sx(0)
-def_swap_ecr.rz(-pi, 0)
-def_swap_ecr.ecr(0, 1)
-def_swap_ecr.rz(pi / 2, 0)
-def_swap_ecr.sx(0)
+def_swap_ecr = QuantumCircuit(q)
 def_swap_ecr.rz(-pi / 2, 0)
+def_swap_ecr.sx(1)
 def_swap_ecr.ecr(0, 1)
-def_swap_ecr.rz(-pi / 2, 0)
+def_swap_ecr.rz(-pi / 2, 1)
 def_swap_ecr.sx(0)
+def_swap_ecr.ecr(1, 0)
 def_swap_ecr.rz(-pi / 2, 0)
-def_swap_ecr.rz(pi / 2, 1)
 def_swap_ecr.sx(1)
-def_swap_ecr.rz(-pi / 2, 1)
+def_swap_ecr.ecr(0, 1)
 _sel.add_equivalence(SwapGate(), def_swap_ecr)
 
 # SwapGate