The development of a nanocrystalline structure in a rapidly quenched Fe73.5Cu1Nb3Si13.5B9 alloy was studied as a function of the duration of annealing at 540°C using the correlational magnetometry method based on the law of magnetization approach to saturation. A distinctive property of this method is the possibility of obtaining information on the structural state of systems with random magnetic anisotropy by predominantly magnetic measurements. The values of individual constants of local magnetic anisotropy and characteristic sizes of the regions of correlation of the anisotropy axes for the amorphous and crystalline phases of the FINEMET alloy were obtained in this study. The variation of these parameters as functions of the annealing duration allowed us to reveal specific features of the crystallization process of the alloy, in particular, to detect the superlattice ordering in the crystalline phase, as well as to relate the structure transformations to the corresponding changes in the magnetic properties.