This paper proposes a new thinning algorithm and proves its validity. This new thinning algorithm can solve the problems explored in one-pass algorithm[5]. A processor suitable for this thinning algorithm is designed to operate on single cycle per iteration. And it also has capability of handling the variable-width input image. Flexible and high-speed operation of this processor shown its applicability in many applications. window has been regarded as optimal size, but it doesn't guarantee the connectedness over the edges of input pattern. Hence, additional windows are used to extract better skeleton. Although these windows show improved results, they still exhibit end-point reduction and disconnected feature in specific condition. In this paper, a modified algorithm is proposed and estimated. Since many thinning algorithms concentrate on the performance of algorithm itself, it is often noted that an algorithm is not easily implemented due to cost and/or technical limitations. Moreover, existing hardware processors are designed to operate only for the fixed image-width, which necessitates the time consuming "normalization process". Now we propose a thinning processor that is flexible over an image-width. Experimental results show its outstanding applicability in various pattern recognition systems.