Character segmentation is a necessary preprocessing step for character recognition in many handwritten word recognition systems. The most difficult case in character segmentation is the cursive script. Fully cursive nature of Bangla handwriting, the natural skewness in words poses some challenges for automatic character segmentation. In this article a novel approach to skew detection, correction as well as character segmentation has been presented for handwritten Bangla words as a test case. Segmenting points are extracted on the basis of some patterns observed in the handwritten words. With these segmenting points a graphical path (hereafter referred to as a candidate path) has been constructed. The handwritten words contain some consistent and also inconsistent skewness. Our algorithm can cope with both types of skewness at a time. Further the method is so direct that with the help of a candidate path one can handle both skew correction and segmentation successfully. the algorithm has been tested on a database prepared for laboratory use. The method yields fairly good results for this database.