Melt-spun Fe63 Co21 B15Cu ribbons were annealed at temperatures between 573 K and 623 K in longitudinal and transverse-magnetic field in order to prepare a representative set of relaxed amorphous and partially crystallized samples having uniaxial anisotropy. The optimal magnetic characteristics for the relaxation sensor were obtained after longitudinal field annealing for 1 h at 593 K, which corresponds to early crystallization stage in the heat treated amorphous material. The magnetic flux density after such heat treatment reaches 1.83 T and the value of coercive field is 4.2 A/m. The corresponding relaxation characteristics obtained by using ferroprobe designed as a flat, double-layer coil tightly surrounding the ribbon core with the dimensions of 60 × 3 mm show good prospects for the potential use of these alloys as core materials in the relax-type fluxgate magnetometers mainly due to the extending of their linear measuring range as compared to the currently used commercial materials while keeping the similar sensitivity.