We propose a constructive procedure to design a Luenberger observer to estimate a linear multiple linear state functional for a linear time-invariant system. Among other features the proposed design algorithm is not based on the solution of a Sylvester equation nor on the use of canonical state space forms. The design is based on the solution set of a linear equation and a realization method. The consistency of this equation and the stability of the observer can be used as a functional observability test. (C) 2016 Published by Elsevier Ltd.