diff --git a/doc/download.xml b/doc/download.xml
index def4273..cf8548c 100644
--- a/doc/download.xml
+++ b/doc/download.xml
@@ -68,6 +68,8 @@ The following components are supported.
   that is a local filename,
   and the function writes the downloaded contents to this file;
   the returned record does not have a <C>result</C> component in this case.
+  <P/>
+  If the download fails then this file is not left behind.
 </Item>
 <Mark><C>verifyCert</C></Mark>
 <Item>
diff --git a/lib/download.gi b/lib/download.gi
index 1e01b2e..e051763 100644
--- a/lib/download.gi
+++ b/lib/download.gi
@@ -125,10 +125,16 @@ Add( Download_Methods, rec(
       res:= ValueGlobal( "SingleHTTPRequest" )( domain, port, "GET", uri,
                 rec( Host:= authority ), false, false );
     fi;
-    if res.statuscode = 0 then
-      return rec( success:= false,
-                  error:= res.status );
-    elif res.statuscode >= 400 then
+    if res.statuscode = 0 or res.statuscode >= 400 then
+      # 'SingleHTTPRequest' has already written the response body, for example
+      # an error page, to the target file; remove it.
+      if IsBound( opt.target ) and IsString( opt.target ) and
+         IsExistingFile( opt.target ) then
+        RemoveFile( opt.target );
+      fi;
+      if res.statuscode = 0 then
+        return rec( success:= false, error:= res.status );
+      fi;
       return rec( success:= false,
                   error:= Concatenation( "HTTP error code ",
                                          String( res.statuscode ) ) );
@@ -219,6 +225,11 @@ Add( Download_Methods, rec(
     code:= Process( DirectoryCurrent(), exec, InputTextNone(), outstream, args );
     CloseStream( outstream );
     if code <> 0 then
+      # curl may have created the target file; remove it, as wget's method does
+      if IsBound( opt.target ) and IsString( opt.target ) and
+         IsExistingFile( opt.target ) then
+        RemoveFile( opt.target );
+      fi;
       return rec( success:= false,
                   error:= Concatenation( "Process returned ", String( code ) ) );
     elif not ( IsBound( opt.target ) and IsString( opt.target ) ) then
@@ -270,6 +281,13 @@ InstallMethod( Download,
         if res.success = true then
           return res;
         fi;
+        # A failed method may have left a partial or bogus target file behind.
+        # Remove it here, so that the guarantee holds for every method,
+        # including ones added to 'Download_Methods' from outside.
+        if IsBound( opt.target ) and IsString( opt.target ) and
+           IsExistingFile( opt.target ) then
+          RemoveFile( opt.target );
+        fi;
         Info( InfoUtils, 2, "Download method ", r.name, " failed with\n",
               "#I    ", res.error );
         Add( errors, Concatenation( r.name, ": ", res.error ) );
diff --git a/tst/download.tst b/tst/download.tst
index e52cc6e..f94824e 100644
--- a/tst/download.tst
+++ b/tst/download.tst
@@ -139,6 +139,26 @@ gap> res1:= Download( url, rec( maxTime:= 5 ) );;
 gap> res1.success = true;
 true
 
+##  A failed download must not leave the target file behind,
+##  whichever method was used.
+gap> file:= Filename( DirectoryTemporary(), "target" );;
+gap> for r in meths do
+>      res1:= r.download( Concatenation( baseurl, "/missing" ),
+>                         rec( target:= file ) );
+>      if res1.success = true then
+>        Print( "unexpected success for ", r.name, "\n" );
+>      elif IsExistingFile( file ) then
+>        Print( "leftover target file after ", r.name, "\n" );
+>        RemoveFile( file );
+>      fi;
+>    od;
+gap> res1:= Download( Concatenation( baseurl, "/missing" ),
+>                     rec( target:= file ) );;
+gap> res1.success = false;
+true
+gap> IsExistingFile( file );
+false
+
 ##  test errors and redirects
 gap> res1:= Download( Concatenation( baseurl, "/missing" ) );;
 gap> res1.success = false;