Index: Lib/test/test_atexit.py
===================================================================
--- Lib/test/test_atexit.py	(Revision 87703)
+++ Lib/test/test_atexit.py	(Arbeitskopie)
@@ -65,6 +65,14 @@
 
         self.assertRaises(TypeError, atexit._run_exitfuncs)
 
+    def test_raise_unnormalized(self):
+        # Issue #10756: Make sure that an unnormalized exception is
+        # handled properly
+        atexit.register(lambda: 1 / 0)
+
+        self.assertRaises(ZeroDivisionError, atexit._run_exitfuncs)
+        self.assertIn("ZeroDivisionError", self.stream.getvalue())
+
     def test_stress(self):
         a = [0]
         def inc():
Index: Modules/atexitmodule.c
===================================================================
--- Modules/atexitmodule.c	(Revision 87703)
+++ Modules/atexitmodule.c	(Arbeitskopie)
@@ -72,6 +72,7 @@
             PyErr_Fetch(&exc_type, &exc_value, &exc_tb);
             if (!PyErr_ExceptionMatches(PyExc_SystemExit)) {
                 PySys_WriteStderr("Error in atexit._run_exitfuncs:\n");
+                PyErr_NormalizeException(&exc_type, &exc_value, &exc_tb);
                 PyErr_Display(exc_type, exc_value, exc_tb);
             }
         }