The fact that the majority of the youngest radio pulsars are surrounded by expanding supernova remnants is strong evidence that neutron stars are produced in the supernovae of massive stars. In many cases, the pulsar appears significantly offset from the geometric centre of the supernova remnant, indicating that the neutron star has moved away from the site of the explosion with a substantial space velocity since birth. Here we show that the these offsets show an overwhelming preference for one sign in terms of Galactic longitude, a result that has important implications for the number of genuine associations. The origin of this statistically significant effect may lie in a differential Galactic rotational velocity between stars and gas in the interstellar medium.