Abstract: This study proposes a new methodology for Error diffused bi-level image compression algorithm. The existing JBIG shows relatively low performance in compressing error-diffused bi-level images. The new method suggests Bayes theorem for showing high performance in error diffused bi-level image compression. By doing so we can improve the resolution and compression factor of the error diffused bi-level images. This method is quite fruitful when we use error diffused bi-level images in the file.