This paper describes an algorithm for finding faces within an image. The basis of the algorithm is to run an observation window at all possible positions, scales and orientation within the image. A non-linear support vector machine is used to determine whether or not a face is contained within the observation window. The non-linear support vector machine operates by comparing the input patch to a set of support vectors (which can be thought of as face and anti-face templates). Each support vector is scored by some non-linear function against the observation window and if the resulting sum is over some threshold a face is indicated. Because of the huge search space that is considered, it is imperative to investigate ways to speed up the support vector machine. Within this paper we suggest a method of speeding up the non-linear support vector machine. A set of reduced set vectors (RV?s) are calculated from the support vectors. By considering the RV?s sequentially, and if at any point a face is deemed too unlikely to cease the sequential evaluation, obviating the need to evaluate the remaining RV?s. The idea being that we only need to apply a subset of the RV?s to eliminate things that are obviously not a face (thus reducing the computation). The key then is to explore the RV?s in the right order and a method for this is proposed.