function GetInetFile(const fileURL, FileName: String): boolean;
var
  hSession, hURL: HInternet;
  Buffer: array[1..1024] of Byte;
  BufferLen: DWORD;
  f: File;
  sAppName: String;
begin
  Result:=false;
  sAppName:=ExtractFileName(Application.ExeName);
  hSession:=InternetOpen(PChar(sAppName),INTERNET_OPEN_TYPE_PRECONFIG,nil,nil,0);
  try
    hURL:=InternetOpenURL(hSession, PChar(fileURL), nil, 0, 0, 0);
    try
      AssignFile(f,FileName);
      ReWrite(f,1);
      repeat
        InternetReadFile(hURL,@Buffer,SizeOf(Buffer),BufferLen);
        BlockWrite(f,Buffer,BufferLen);
        Vers.ProgressBar1.Position:=Vers.ProgressBar1.Position+BufferLen;
        Application.ProcessMessages;
      until
        BufferLen = 0;
      CloseFile(f);
      Result:=True;
    finally
      InternetCloseHandle(hURL);
    end;
  finally
    InternetCloseHandle(hSession);
  end;
end;

if GetInetFile('http://tcprog.mcdir.ru/myprogram.exe',ExtractFilePath(Application.ExeName)+'/myprogram.exe') = true then
.....