A new type of renormalization-group approach is suggested to treat the structure and properties of the Frenkel-Kontorova (discrete sine-Gordon) model ground states. Special attention is devoted to the incommensurate structures where the transition by breaking of analyticity of the hull function (pinning-depinning transition) occurs when the strength of the periodic potential is varied. The method gives for a particular incommensurability-the 'golden mean' one-a critical value of the potential strength one-and-a-half times larger than the exact value obtained by Aubry et al. (1982, 1983) by numerical methods. The critical index of correlation length coincides within a few per cent accuracy with its exact value.