In this paper we present a modification of the CORDIC algorithm which reduces the number of iterations almost to half by merging two successive iterations of the basic algorithm. The two coefficients per iteration are obtained with only a small increase in the cycle time by estimating one of the coefficients. A correcting iteration method is used to correct the possible errors produced by the estimate. Moreover, the modified iteration permits the reduction of the number of cycles required for the compensation of the scaling factor. The resulting architecture is word serial, working both in rotation and vectoring operation modes, presenting a low latency in comparison with the classical CORDIC approach.