Side-channel attacks(SCA) may exploit leakage information to break cryptosystems. In this paper we present a new SCA resistant Elliptic Curve scalar multiplication algorithm. The proposed algorithm, builds a sequence of bit-strings representing the scalar k, characterized by the fact that all bit-strings are different from zero; this property will ensure a uniform computation behavior for the algorithm, and thus will make it secure against simple power analysis attacks(SPA). With other randomization techniques, the proposed countermeasures do not penalize the computation time. The proposed scheme is more efficient than M(O)ller one, its cost being about 5% to 10% smaller than M(O)ller one.