The relationship between effective permeability and the remanence ratio of an Fe-based amorphous alloy (Metglas 2605S3A) is investigated over a wide frequency range, in an effort to understand magnetization behavior of the alloy. In the frequency range from 1 to 200 kHz, the permeability is maximum at the remanence ratio of 0.4-0.5 and, at frequencies over 500 kHz, the correlation with negative coefficients emerges indicating that the permeability decreases with the remanent ratio, except for the ribbon coated with an insulating layer of MgO which exhibits both high values of the effective permeability and remanence ratio. It is considered from the correlation results that the boundary at which the dominant magnetization mechanism changes from domain wall motion to spin rotation is near 500 kHz. The core loss is also investigated as a function of annealing time when the samples are annealed at a fixed temperature of $435^{circ}C$. The core loss in most cases decreases with the annealing time, the degree of the loss may consist of the hysteresis loss and anomalous eddy current loss. The two loss components are considered to be of similar magnitudes at low frequencies while, at high frequencies, the dominant contribution to the total loss is the anomalous loss.