A new version of digital signature scheme (DSS) has been proposed in this work. This version has used a new concept of linear algebra which is called the integer matrix of Fibonacci numbers with size 2×2 (IFM2×2). The main point is to use the IFM2×2 with its right power (RPIFM2×2) for creating the digital signature. The verification is done of this signature using the computations of the RPIFM2×2 as well. New implemented results on the proposed DSS-RPIFM2×2 have been done using Python programming. The issue of the security has been determined based on the randomization for generating the IFM2×2 of the elements over a field Fp of prime numbers secretly. The DSS- PRIFM2×2 version is proposed to be a more secure for sending the signed messages and to avoid forging the signature of them. Thus, the proposed version of DSS- RPIFM2×2 considers as a bright point for more authenticity, integrity and non-repudiation in compare to the previous communication schemes.