This paper considers an iterative procedure to design a minimum possible order unknown input functional observer for linear time-invariant systems. Necessary and sufficient conditions for the existence of the observer are given. The proposed procedure is simple and is based neither on the solution of a generalized Sylvester equation nor canonical forms. This procedure can be easily implemented due to its incremental form. The main feature of our procedure is then the simplicity of the design. Moreover, in the case of a single functional to be observed, a minimum order stable linear unknown input functional observer is obtained.