Minutiae feature based fingerprint recognition systems heavily depend on the pixel-wise operations on skeletonized fingerprint image. The skeletonization is done by proper thinning algorithms. The minutiae features (Ridge endings and Bifurcations) can be extracted from a finely skeletonized fingerprint image. The efficiency of the thinning method determines the quality of the image skeleton and the accuracy in feature extraction. Therefore a new skeletonization technique is proposed. The new skeletonization algorithm uses a number of masks to check whether the pixel is on the boundary or not. Once the pixel is marked as boundary pixel, then the algorithm eliminates that pixel and repeat the process to get the fingerprint image skeleton of one-pixel width. The proposed system is computationally efficient and it preserves the connectivity of the pixels in the image.