Reading text file with CStdioFile.ReadString

I'm trying to read a text file using CStdioFile, and finally got it to work
about right...not sure what I was missing, but eventually I got all the lines
into a string and was able to set the window text of my CRichEditView with
this

    CStdioFile file;
    file.Open(fname,CFile::modeRead|CFile::typeText);

    CString stext;
    CString buffer;

    while (file.ReadString(stext) != FALSE)
    {
        buffer += stext;
        buffer += "\n";
        file.ReadString(stext);

    }
    file.Close();

    SetWindowText(buffer);

The issues I have is that the LAST line of the text file seems to get an
extra space added to the beginning of the line. Given I struggled to get
this far in what *should* be a near trivial exercise, I must be missing
something.

From what I read in the documentation, the CString version of ReadString
does NOT return the end of line character. So that's why I add it. But why
would the LAST line get and extra space at the START of the line, and no
other line is changed???

Thanks for any insight. VC++ 6.0 on Win XP home, if that matters...