This papre presents the RDM algorithm for composition of bit. After this, we propose a digital signature scheme for facsimile document using RDM algorithm. We modify the even-odd feature in distance of changing pel between coding line and multiple reference line which have been scanned before, and run-length in coding line. The time to take in signature is reduced by spreading of signature. Non-repudiation in origin, the 3rd condition of digital signature is realized by proposed digital signature scheme. The transmitter embeds the signature secretly and tensfers it, and the receiver makes a check of any forgery on the signature and the document. This scheme is compatible with the ITU-T.4(G3 or G4 facsimile standard). The total amount of data transmitted and the quality of image are about the same to that of the original document, thus a third party does not notics signature embeded on the document.