The minimum–phase requirement restricts that filter has all its zeros on or inside the unit circle. As a result the filter does not have a linear phase. It is well known that the sharpening technique can be used to simultaneous improvements of both the passband and stop-band of a linear-phase FIR filters and cannot be used for other types of filters. In this paper we demonstrate that the sharpening technique can also be applied to minimum-phase filters, after small modification. The method is illustrated with one practical examples of design.