In this study, we have obtained a step size strategy based on Picard-Lindelöf theorem and error analysis for the numeric integration of Cauchy problems in a region where the solutions of Cauchy problems exist and are unique. We have given an algorithm which calculates step size based on Picard-Lindelöf theorem and error analysis and obtains approximate solutions. The strategy and algorithm are modifications of the strategy and algorithm in [G. Çelik Ki{dotless}zi{dotless}lkan, K. Aydi{dotless}n, Step size strategy based on error analysis, Selcuk University Science and Art Faculty Journal of Science 25 (2005) 79-86 (in Turkish)]. © 2006 Elsevier Inc. All rights reserved.