Coordinate Rotation Digital Computer (CORDIC) is a unified arithmetic algorithm that allows efficient VLSI implementation of several elementary functions. Many special-purpose systems for real-time signal processing application use a fixed-point representation of numbers due to the ease of implementation. An analysis of fixed-point CORDIC in the Y-reduction mode, which allows computation of the inverse tangent function, shows that unnormalized input values can result in large numerical errors. This paper presents a method to integrate the normalization operatioin with CORDIC iterations for efficient implementation in 0(n^1.5) hardware.