Recent studies have demonstrated the importance of protecting the hardware implementations of cryptographic functions against side channel and fault attacks. In last years, very efficient implementations of modular arithmetic have been done in RNS (RSA, ECC, pairings) as well on FPGA as on GPU. Thus the protection of RNS Montgomery modular multiplication is a crucial issue. For that purpose, some techniques have been proposed to protect this RNS operation against side channel analysis. Nevertheless, there are still no effective and generic approaches for the detection of fault injection, which would be additionnally compatible with a leak resistant arithmetic. This paper proposes a new RNS Montgomery multiplication algorithm with fault detection capability. A mathematical analysis demonstrates the validity of the proposed approach. Moreover, an architecture that implements the proposed algorithm is presented. A comparative analysis shows that the introduction of the proposed fault detection technique requires only a limited increase in area.