In several encryption algorithms, the key exchange scheme (KES) type: Diffie-Hellman is used as a fundamental tool. In this paper, a new KES model has been proposed as an alternative contribution for using the matrix of Fibonacci numbers (IFM2×2). On the proposed model, the private keys are created as the IFMs2×2 through selecting the Fibonacci numbers (FNs) randomly over Fp, where p is a prime. The power IFMs2×2 from left (right) side is calculated (LPIFM2×2(RPIFM2×2)). These matrices are also used to compute public keys. A new algorithm of the proposed scheme, namely IFM2×2-KES, is presented in this work. New results are displayed for small parameter values, implemented in Python. The difficult computations of LPIFM2×2 and RPIFM2×2 simultaneously determine the security of the proposed algorithm. The proposed IFM2×2-KES is considered a bright point for the communication scheme.