The Coordinate Rotation Digital Computer (CORDIC) is a well-known arithmetic computing technique for vector rotation, without performing multiplications. For applications where the angle of rotation is known in advance, the angle recoding scheme for CORDIC speeds up the execution of the algorithm by reducing the total number of elementary iterations required for rotating the vector. In this paper, the angle recoding scheme has been extended for those applications where the rotational angle is not known a priori. This is accomplished by reducing the number of search iterations in the Greedy algorithm used for recoding the angle. Then, this modified Greedy algorithm is executed along with the CORDIC iterations to recode the rotational angle in real-time. Finally, a novel scheme for determining the variable scaling factor arising due to the CORDIC iterations has been proposed. When angle recoding is performed in real-time along with the CORDIC iterations, this scaling factor is not known a priori. The proposed scheme determines the scaling factor very efficiently, without introducing any additional computational delay in the CORDIC algorithm.