This paper presents a new implementation of a floating-point divider unit with a competitive performance and reduced area based on proposed modifications to the recursive equations of Goldschmidt algorithm. The Goldschmidt algorithm takes advantage of parallelism in the Newton-Raphson method with the same quadratic convergence. However, recursive equations in the Goldschmidt algorithm consist of a series of multiplications with full-precision operands, and it suffers from large area consumption. In this paper, the recursive equations in the algorithm are modified to replace full-precision multipliers with smaller multipliers and squarers. Implementations of floating-point reciprocal and divider using the modification are presented. Synthesis result shows around 20% to 40% area reduction when it is compared to the implementation based on the conventional Goldschmidt algorithm.