A common problem in tasks involving the integration of spatial information from multiple senses, or in sensorimotor coordination, is that different modalities represent space in different frames of reference. Coordinate transformations between different reference frames are therefore required. One way to achieve this relies on the encoding of spatial information with population codes. The set of network responses to stimuli in different locations (tuning curves) constitutes a set of basis functions that can be combined linearly through weighted synaptic connections to approximate nonlinear transformations of the input variables. The question then arises: how is the appropriate synaptic connectivity obtained? Here we show that a network of spiking neurons can learn the coordinate transformation from one frame of reference to another, with connectivity that develops continuously in an unsupervised manner, based only on the correlations available in the environment and with a biologically realistic plasticity mechanism (spike timing-dependent plasticity).