This paper addresses a discussion about Unknown Input Observers (UIO) for Linear Parameter Varying (LPV) systems designed classically by using the polytopic representation. It is illustrated that even if the rank conditions ensuring the existence of an UIO are satisfied, the design may fail, due to the polytopic representation of the LPV system. In this paper a new design approach is proposed via two different UIOs for a class of LPV systems with parameter dependent output equation. It is based on parameter algebraic matrix equations and LMI conditions. Examples are provided in order to illustrate the performances of the proposed approach.