diff --git a/IPython/nbconvert/filters/latex.py b/IPython/nbconvert/filters/latex.py
index f366702..e03a945 100755
--- a/IPython/nbconvert/filters/latex.py
+++ b/IPython/nbconvert/filters/latex.py
@@ -60,4 +60,4 @@ def escape_latex(text):
         text = pattern.sub(replacement, text)
 
     return text
-
+    
diff --git a/IPython/nbconvert/filters/strings.py b/IPython/nbconvert/filters/strings.py
index 97ef3a3..77253ca 100755
--- a/IPython/nbconvert/filters/strings.py
+++ b/IPython/nbconvert/filters/strings.py
@@ -122,19 +122,22 @@ def strip_dollars(text):
     return text.strip('$')
 
 
-files_url_pattern = re.compile(r'(src|href)\=([\'"]?)files/')
+files_url_pattern = re.compile(r'(src|href)\=([\'"]?)/?files/')
+markdown_url_pattern = re.compile(r'(!?)\[(?P<caption>.*?)\]\(/?files/(?P<location>.*?)\)')
 
 def strip_files_prefix(text):
     """
-    Fix all fake URLs that start with `files/`,
-    stripping out the `files/` prefix.
+    Fix all fake URLs that start with `files/`, stripping out the `files/` prefix.
+    Applies to both urls (for html) and relative paths (for markdown paths).
     
     Parameters
     ----------
     text : str
         Text in which to replace 'src="files/real...' with 'src="real...'
     """
-    return files_url_pattern.sub(r"\1=\2", text)
+    cleaned_text = files_url_pattern.sub(r"\1=\2", text)
+    cleaned_text = markdown_url_pattern.sub(r'\1[\2](\3)', cleaned_text)
+    return cleaned_text
 
 
 def comment_lines(text, prefix='# '):
diff --git a/IPython/nbconvert/filters/tests/test_latex.py b/IPython/nbconvert/filters/tests/test_latex.py
index a66d0f5..cc324b1 100644
--- a/IPython/nbconvert/filters/tests/test_latex.py
+++ b/IPython/nbconvert/filters/tests/test_latex.py
@@ -41,5 +41,3 @@ class TestLatex(TestsBase):
     def _try_escape_latex(self, test, result):
         """Try to remove latex from string"""
         self.assertEqual(escape_latex(test), result)
-
-
diff --git a/IPython/nbconvert/filters/tests/test_strings.py b/IPython/nbconvert/filters/tests/test_strings.py
index 9fc6d63..f93749c 100644
--- a/IPython/nbconvert/filters/tests/test_strings.py
+++ b/IPython/nbconvert/filters/tests/test_strings.py
@@ -87,7 +87,20 @@ class TestStrings(TestsBase):
             ('/files', '/files'), 
             ('test="/files"', 'test="/files"'), 
             ('My files are in `files/`', 'My files are in `files/`'),
-            ('<a href="files/test.html">files/test.html</a>', '<a href="test.html">files/test.html</a>')]
+            ('<a href="files/test.html">files/test.html</a>', '<a href="test.html">files/test.html</a>'),
+            ('<a href="/files/test.html">files/test.html</a>', '<a href="test.html">files/test.html</a>'),
+            ("<a href='files/test.html'>files/test.html</a>", "<a href='test.html'>files/test.html</a>"),
+            ('<img src="files/url/location.gif">', '<img src="url/location.gif">'),
+            ('<img src="/files/url/location.gif">', '<img src="url/location.gif">'),
+            ('hello![caption]', 'hello![caption]'),
+            ('hello![caption](/url/location.gif)', 'hello![caption](/url/location.gif)'),
+            ('hello![caption](url/location.gif)', 'hello![caption](url/location.gif)'),
+            ('hello![caption](url/location.gif)', 'hello![caption](url/location.gif)'),
+            ('hello![caption](files/url/location.gif)', 'hello![caption](url/location.gif)'),
+            ('hello![caption](/files/url/location.gif)', 'hello![caption](url/location.gif)'),
+            ('hello [text](/files/url/location.gif)', 'hello [text](url/location.gif)'),
+            ('hello [text space](files/url/location.gif)', 'hello [text space](url/location.gif)'),
+        ]
         for test in tests:
             self._try_files_prefix(test[0], test[1])
 
diff --git a/IPython/nbconvert/templates/latex/latex_base.tplx b/IPython/nbconvert/templates/latex/latex_base.tplx
index 97a67a5..21bb5e7 100644
--- a/IPython/nbconvert/templates/latex/latex_base.tplx
+++ b/IPython/nbconvert/templates/latex/latex_base.tplx
@@ -202,7 +202,7 @@ This template does not define a docclass, the inheriting class must define this.
     ((* elif cell.level == 6 -*))
         ((* block h6 -*))\\*\textit((* endblock h6 -*))
     ((*- endif -*))
-    {((( cell.source | replace('\n', ' ') | citation2latex | markdown2latex )))}
+    {((( cell.source | replace('\n', ' ') | citation2latex | strip_files_prefix | markdown2latex )))}
 
 ((* endblock headingcell *))
 
@@ -215,7 +215,7 @@ This template does not define a docclass, the inheriting class must define this.
 
 % Render markdown
 ((* block markdowncell scoped *))
-    ((( cell.source | citation2latex | markdown2latex )))
+    ((( cell.source | citation2latex | strip_files_prefix | markdown2latex )))
 ((* endblock markdowncell *))
 
 % Don't display unknown types