In FIR (Finite Impulse Response) filter applications, Nth-band F]U digital filters are known to be important due to their reduced computational requirements. The conventional methods for designing F]U filters use iterative approaches such as the well-known Parks-Mcclellan algorithm. The Parks-Mcclellan algorithm is also used to design Nth-band FIR digital filters. But a disadvantage of the Parks-Mcclellan algorithm is that it needs a good amount of design time. This paper describes a direct design method for Nth-band FIR Filters using Chebyshev polynomials, which provides a reduced design time over indirect methods such as the Parks-Mcclellan algorithm. The response of the resulting filter is equiripple in passband. Our proposed method produces a passband response that is equripple to within a minuscule error, comparable to that of the Parks-Mcclellan algorithm.