In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log(2)r/phi(k), where phi(.) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from left perpendicularlog(2)rright perpendicular to left perpendicularlog(2)(t - 1)right perpendicular. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "chi". For the curve, this paper gives integer variable chi-based Ate pairing that achieves the lower bound by reducing it to left perpendicularlog(2) chi right perpendicular.