We present a robust fuzzy clustering method that utilizes a sequential cluster extraction scheme. In contrast to heuristic sequential methods, our algorithm is derived from an optimization problem and is an iterative solution to it. Our method is non-parametric and includes no heuristic parameter, and can deal with asymmetric similarity data. The determination of the number of clusters is simple and is based on a monotonic property of extracted cluster volumes. Our method can extract arbitrarily shaped clusters by extending the measure of distance between data to a shortest path length. The performance of the method is demonstrated for clustering of an image database and the segmentation of images.