On smart-cards, Elliptic Curve Cryptosystems (ECC) can be vulnerable to Side Channel Attacks such as the Refined Power Analysis (RPA). This attack takes advantage of the apparition of special points of the form (0,
). In this paper, we propose a new countermeasure based on co-
formulæ and an extension of the curve isomorphism countermeasure. It permits to transform the base point
) into a base point
′ = (0,
′), which, with −
′, are the only points with a zero
-coordinate. In such case, the RPA cannot be applied. Moreover, the cost of this countermeasure is very low compared to other countermeasures against RPA.