Handwritten character recognition has been an intensive research for last decade. A handwritten character recognition fuzzy system with an automatically generated rule base possesses the features of flexibility, efficiency and online adaptability. A major requirement of such a fuzzy system for either online or offline handwritten character recognition is, the segmentation of individual characters into meaningful segments. Then these segments can be used for the calculation of fuzzy features and the recognition process. This paper describes a new segmentation algorithm for offline handwritten character segmentation, which segments the individual handwritten character skeletons into meaningful segments. Therefore, this algorithm is a good candidate for an offline handwritten character recognition fuzzy system.