diff --git a/qiskit/transpiler/passes/routing/cython/stochastic_swap/utils.pxd b/qiskit/transpiler/passes/routing/cython/stochastic_swap/utils.pxd
index d45676f55f0c..f41e16fcea63 100644
--- a/qiskit/transpiler/passes/routing/cython/stochastic_swap/utils.pxd
+++ b/qiskit/transpiler/passes/routing/cython/stochastic_swap/utils.pxd
@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 #!python
 #cython: language_level = 3, cdivision = True, nonecheck = False
 #distutils: language = c++
@@ -14,6 +13,7 @@
 # Any modifications or derivative works of this code must retain this
 # copyright notice, and modified files need to carry a notice indicating
 # that they have been altered from the originals.
+
 from libcpp.vector cimport vector
 
 # Numeric layout --------------------------------------------------------------
diff --git a/tools/verify_headers.py b/tools/verify_headers.py
index a904096ecfee..a56ab19a0009 100755
--- a/tools/verify_headers.py
+++ b/tools/verify_headers.py
@@ -11,6 +11,8 @@
 # copyright notice, and modified files need to carry a notice indicating
 # that they have been altered from the originals.
 
+"""Utility script to verify qiskit copyright file headers"""
+
 import argparse
 import multiprocessing
 import os
@@ -22,6 +24,7 @@
 
 
 def discover_files(code_paths):
+    """Find all .py, .pyx, .pxd files in a list of trees"""
     out_paths = []
     for path in code_paths:
         if os.path.isfile(path):
@@ -30,12 +33,17 @@ def discover_files(code_paths):
             for directory in os.walk(path):
                 dir_path = directory[0]
                 for subfile in directory[2]:
-                    if subfile.endswith(".py") or subfile.endswith(".pyx"):
+                    if (
+                        subfile.endswith(".py")
+                        or subfile.endswith(".pyx")
+                        or subfile.endswith(".pxd")
+                    ):
                         out_paths.append(os.path.join(dir_path, subfile))
     return out_paths
 
 
 def validate_header(file_path):
+    """Validate the header for a single file"""
     header = """# This code is part of Qiskit.
 #
 """
@@ -70,7 +78,7 @@ def validate_header(file_path):
     return (file_path, True, None)
 
 
-def main():
+def _main():
     default_path = os.path.join(
         os.path.dirname(os.path.dirname(os.path.abspath(__file__))), "qiskit"
     )
@@ -80,7 +88,7 @@ def main():
         type=str,
         nargs="*",
         default=[default_path],
-        help="Paths to scan by default uses ../qiskit from the" " script",
+        help="Paths to scan by default uses ../qiskit from the script",
     )
     args = parser.parse_args()
     files = discover_files(args.paths)
@@ -96,4 +104,4 @@ def main():
 
 
 if __name__ == "__main__":
-    main()
+    _main()