This technical note solves the problem to detect and isolate faults in linear periodic discrete-time systems. A residual generator is designed through a suitable unknown input observer with the requirement that each residual should be sensitive only to one fault and, simultaneously, insensitive to the other faults that can affect the system, and with the additional requirement of rho-detectability, that is the transition matrix of its relative error system has all eigenvalues smaller than rho, in modulus, for a given positive rho <= 1. The solution is based on geometric tools, and it makes use of the outer observable subspace notion.