Interrelation between magnetic properties and surface crystallization and structural heredity of the melt was studied using amorphous ribbons of Fe81B13Si4C2 soft magnetic alloy as an example. The study showed that obtaining optimum magnetic properties of the alloys by heat treatment required the formation of a surface amorphous-crystalline layer ≈30-50 nm thick. The physical nature of this effect consists in the creation of tensile stresses in the surface layer of the amorphous matrix due to the formation of crystalline grains, which increases the number of magnetic domains with in-plane magnetization and decreases domain wall stability. Heat treatment at 380°C for 10 min and cooling at a rate of 15 K/min enables higher magnetic properties to be obtained for less homogeneous alloys (without overheating treatment of the melt before amorphization) due to the formation of a surface amorphous-crystalline layer of optimum thickness. The inferior magnetic properties of ribbons with higher structural homogeneity (after heat treatment of the melt) are likely to be due to the lower activity of diffusion processes resulting in a decrease in the rate of internal stress relief upon annealing and delay of crystallization. The difference in the time behavior of magnetic properties between the two ribbon samples under study can also be attributed to the peculiarities of crystallization processes that occur at room temperature. The time stability of magnetic properties of the ribbon can be improved significantly by magnetic annealing.