In comparative studies of constrained optimization methods the equality contrained recursive quadratic programming procedure has performed very favorably, particularly in terms of required computer time for execution. Biggs has formulated a strategy based on a quadratic penalty function and proved the global convergence of the method. This paper reformulates the procedure based on a Lagrangian penalty function leading to improved performance and reduced sensitivity to the algorithm parameters. The formulation and algorithm are described herein and global convergence is demonstrated. Evaluation results on several test problems are presented to allow comparisons with other algorithms of the same type.