Research efforts have produced many algorithms for fast pairing computation and several efficient hardware implementations. However, side channel attacks (SCAs) are a serious threat on hardware implementations. Previous works in this area have provided some costly countermeasures against side channel attacks. In this paper, we propose a new countermeasure based on the isomorphism classes in order to secure pairing computation on elliptic curves defined over K with Char(K)≠2, 3. The proposed technique requires only eight additional field multiplications which is negligible compared to the cost of the other known countermeasures.