It is well-established that simple cells in the primate visual cortex can be understood in terms of linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an energy model of the complex cell response. Here we propose an alternative model of the complex cell, based on Gaussian derivatives. It is most important to account for the invariance of the complex response to small shifts of the image. The new model takes a linear combination of the first N derivative filters, at a single position. This combination is made to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model is demonstrated in 1D and 2D, including experiments on natural images. Certain advantages over the Gabor energy model are discussed, including the steerability of the new model. It is noted that the range of spatial invariance depends on the number of available derivatives, which suggests a role for the high-order filters that have been found in the primate visual cortex.