Young pulsars are known to exhibit large space velocities, up to 103 km/s. We propose a new mechanism for the generation of these large velocities based on an asymmetric emission of neutrinos during the supernova explosion. The mechanism involves the resonant spin-flavour precession of neutrinos with a transition magnetic moment in the magnetic field of the supernova. The asymmetric emission of neutrinos is due to the distortion of the resonance surface by matter polarisation effects in the supernova magnetic field. The requisite values of the field strengths and neutrino parameters are estimated for various neutrino conversions caused by their Dirac or Majorana-type transition magnetic moments.