diff --git a/plugin/fugitive.vim b/plugin/fugitive.vim
index ed5c959..2ec473f 100644
--- a/plugin/fugitive.vim
+++ b/plugin/fugitive.vim
@@ -413,10 +413,9 @@ function! FugitiveExtractGitDir(path) abort
     return matchstr(path, '\C^fugitive:\%(//\)\=\zs.\{-\}\ze\%(//\|::\|$\)')
   elseif empty(path)
     return ''
-  elseif path !~# '^/\|^\a\+:'
-    let path = s:Slash(getcwd()) . '/' . path
+  else
+    let path = fnamemodify(path, ':p:h')
   endif
-  let path = fnamemodify(path, ':h')
   let pre = substitute(matchstr(path, '^\a\a\+\ze:'), '^.', '\u&', '')
   if len(pre) && exists('*' . pre . 'Real')
     let path ={pre}Real(path)