We study the formation of the absorption features, called the cyclotron-annihilation lines, in the γ -spectra of the neutron stars (pulsars), owing to the fundamental quantum-electrodynamic effect of the one-photon pair creation in magnetized vacuum. As a result, we substantiate a new method for the determination of the neutron star magnetic fields B based on measuring the interval between the main annihilation and the first cyclotron-annihilation absorption lines. It is found that these lines may be easily resolved, and, consequently, the method is surely applicable if the following conditions are satisfied. (i) A γ -source has to be compact enough and located near a star, but not close to its magnetic poles. For instance, it may be a disc in the plane of a star magnetic equator with latitudinal angular width less than B/4.4 × 10 13 G and radial extent up to 25 per cent of the star radius. (ii) The source is to produce detectable γ -radiation at large angles 60 • to the local magnetic field. Being situated in a closed field line region and having a broad radiation pattern, such a source is not what is usually considered in the context of the polar cap and outer gap models of the pulsar γ -emission dealing with open field lines only. (iii) Magnetic field strength must lie in a certain narrow interval with the centre at ∼(3-4) × 10 12 G. Its width depends on the star orientation and disc radial extend and in the most favourable case is about 20-30 per cent of its lower boundary. Finally, the influence of the star rotation on this method employment is considered and new possibilities arising from forthcoming polarization observations are briefly discussed.