diff --git a/Lib/html/parser.py b/Lib/html/parser.py
index 662e855..dd9c2e1 100644
--- a/Lib/html/parser.py
+++ b/Lib/html/parser.py
@@ -14,7 +14,6 @@
 # Regular expressions used for parsing
 
 interesting_normal = re.compile('[&<]')
-interesting_cdata = re.compile(r'<(/|\Z)')
 incomplete = re.compile('&[a-zA-Z#]')
 
 entityref = re.compile('&([a-zA-Z][-.a-zA-Z0-9]*)[^a-zA-Z0-9]')
@@ -149,8 +148,8 @@
         return self.__starttag_text
 
     def set_cdata_mode(self, elem):
-        self.interesting = interesting_cdata
         self.cdata_elem = elem.lower()
+        self.interesting = re.compile(r'</\s*%s\s*>' % self.cdata_elem, re.I)
 
     def clear_cdata_mode(self):
         self.interesting = interesting_normal
@@ -168,6 +167,8 @@
             if match:
                 j = match.start()
             else:
+                if self.cdata_elem:
+                    break
                 j = n
             if i < j: self.handle_data(rawdata[i:j])
             i = self.updatepos(i, j)
@@ -250,7 +251,7 @@
             else:
                 assert 0, "interesting.search() lied"
         # end while
-        if end and i < n:
+        if end and i < n and not self.cdata_elem:
             self.handle_data(rawdata[i:n])
             i = self.updatepos(i, n)
         self.rawdata = rawdata[i:]
diff --git a/Lib/test/test_htmlparser.py b/Lib/test/test_htmlparser.py
index 1ce4594..87b5060 100644
--- a/Lib/test/test_htmlparser.py
+++ b/Lib/test/test_htmlparser.py
@@ -301,7 +301,27 @@
                                     ("data", content),
                                     ("endtag", element_lower)])
 
+    def test_cdata_with_closing_tags(self):
+        # see issue #13358
+        # make sure that HTMLParser calls handle_data only once for each CDATA.
+        # The normal event collector normalizes  the events in get_events,
+        # so we override it to return the original list of events.
+        class Collector(EventCollector):
+            def get_events(self):
+                return self.events
 
+        content = """<!-- not a comment --> &not-an-entity-ref;
+                  <a href="" /> </p><p> <span></span></style>
+                  '</script' + '>'"""
+        for element in [' script', 'script ', ' script ',
+                        '\nscript', 'script\n', '\nscript\n']:
+            element_lower = element.lower().strip()
+            s = '<script>{content}</{element}>'.format(element=element,
+                                                       content=content)
+            self._run_check(s, [("starttag", element_lower, []),
+                                ("data", content),
+                                ("endtag", element_lower)],
+                            collector=Collector())
 
 class HTMLParserTolerantTestCase(HTMLParserStrictTestCase):
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 8a82b09..513984d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -76,6 +76,8 @@
 Library
 -------
 
+- Issue #13358: HTMLParser now calls handle_data only once for each CDATA.
+
 - Issue #4147: minidom's toprettyxml no longer adds whitespace around a text
   node when it is the only child of an element.  Initial patch by Dan
   Kenigsberg.