This paper presents a new method for devising linear colour-dependent filters based on decomposition of an image into components parallel and perpendicular to a chosen direction in colour space. The components may be separately filtered with linear filters and added to produce an overall result. The paper demonstrates this approach with a colour-selective averager, and then shows that the filter may be implemented without the parallel/perpendicular decomposition by adding the output of two filters, derived in the paper. The approach is based on quaternion algebra and convolution.