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• The trajectories for optimized B s and H c determined by both annealing temperature and time were established. • A relatively larger B s up to 1.74 T and lower H c of 4.9 A/m were found for the present alloy compared to the nanocrystalline alloys with similar Fe content. • It is found that the precipitated α -Fe (Si) grain number density is the main factor to determine the B s A (Fe 0.83 B 0.11 Si 0.02 P 0.03 C 0.01) 99.5 Cu 0.5 glass former was formulated based on Fe 83 B 11 Si 2 P 3 C 1 alloy and a new rapid annealing method was employed to investigate both the temperature and time effect on the improvement of soft magnetic properties of the amorphous alloy ribbon. The results show that the interval between the first and second crystallization temperature is enlarged by Cu addition. There exists an optimal annealing time corresponding to the optimal B s and H c for the ribbon annealed at each temperature. The maximum B s up to 1.74 T and the minimum H c of 4.9 A/m were obtained for the ribbon annealed at 426 °C for 150 s. The grain number density of precipitated α -Fe(Si) is the main factor in determining the B s. Compared to other nanocrystalline alloys with similar Fe content, the present alloy ribbon annealed by the new method shows a higher B s and a lowest H c , which makes it a promising soft magnetic material used in the field of electrical and electronic industries. [ABSTRACT FROM AUTHOR]