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The magnetoimpedance response of the soft amorphous magnetic CoFeNiSiB alloy can be improved by the application of a small magnetic field during the fabrication process. Calorimetric and magnetic (hysteresis loop) behavior as well as magnetoimpedance response of melt-spun ribbons obtained by two different ways of production processes are analyzed in this work. The crystallization dynamics also show small differences. High sensitivities to the applied magnetic field up to 320%/Oe are observed when a small transverse anisotropy is induced in the ribbon sample during the fabrication process under the action of a magnetic field.