diff --git a/Include/pyerrors.h b/Include/pyerrors.h
--- a/Include/pyerrors.h
+++ b/Include/pyerrors.h
@@ -312,6 +312,7 @@
 
 
 /* In sigcheck.c or signalmodule.c */
+PyAPI_FUNC(void) PyErr_AddPendingCheckSignals(void);
 PyAPI_FUNC(int) PyErr_CheckSignals(void);
 PyAPI_FUNC(void) PyErr_SetInterrupt(void);
 
diff --git a/Lib/test/test_sys_settrace.py b/Lib/test/test_sys_settrace.py
--- a/Lib/test/test_sys_settrace.py
+++ b/Lib/test/test_sys_settrace.py
@@ -5,6 +5,8 @@
 import sys
 import difflib
 import gc
+import time
+import signal
 
 # A very basic example.  If this fails, we're in deep trouble.
 def basic():
@@ -480,6 +482,31 @@
         finally:
             sys.settrace(existing)
 
+    def test_exception_raised_in_alarm(self):
+        # Test that an exception raised in an alarm does not remove the trace
+        # function (issue 20601).
+        def trace(frame, event, arg):
+            funcname = frame.f_code.co_name
+            if event == 'call' and funcname == 'f':
+                time.sleep(1)
+            return trace
+
+        def f(): pass
+
+        def handler(*args):
+            1/0
+
+        sys.settrace(trace)
+        signal.signal(signal.SIGALRM, handler)
+        signal.alarm(1)
+        err = None
+        try:
+            f()
+        except ZeroDivisionError as e:
+            err = e
+        self.assertIsInstance(err, ZeroDivisionError)
+        self.assertIs(sys.gettrace(), trace)
+
 
 # 'Jump' tests: assigning to frame.f_lineno within a trace function
 # moves the execution position - it's how debuggers implement a Jump
diff --git a/Modules/signalmodule.c b/Modules/signalmodule.c
--- a/Modules/signalmodule.c
+++ b/Modules/signalmodule.c
@@ -1312,11 +1312,20 @@
 
 
 /* Declared in pyerrors.h */
+/* Add a pending call to check for signals (postponed during tracing). */
+void
+PyErr_AddPendingCheckSignals(void)
+{
+    is_tripped = 1;
+    Py_AddPendingCall(checksignals_witharg, NULL);
+}
+
 int
 PyErr_CheckSignals(void)
 {
     int i;
     PyObject *f;
+    PyThreadState *tstate;
 
     if (!is_tripped)
         return 0;
@@ -1345,7 +1354,13 @@
     if (!(f = (PyObject *)PyEval_GetFrame()))
         f = Py_None;
 
+    tstate = PyThreadState_GET();
+
     for (i = 1; i < NSIG; i++) {
+        /* Postpone signals while evaluating the trace function. */
+        if (tstate->tracing && i != SIGINT)
+            continue;
+
         if (Handlers[i].tripped) {
             PyObject *result = NULL;
             PyObject *arglist = Py_BuildValue("(iO)", i, f);
diff --git a/Python/ceval.c b/Python/ceval.c
--- a/Python/ceval.c
+++ b/Python/ceval.c
@@ -3912,6 +3912,7 @@
     tstate->use_tracing = ((tstate->c_tracefunc != NULL)
                            || (tstate->c_profilefunc != NULL));
     tstate->tracing--;
+    PyErr_AddPendingCheckSignals();
     return result;
 }