This paper discusses the problem of designing an observer to estimate a vector-valued (multi-) linear function of the state of a linear time-invariant system, for the purpose of implementing a feedback control law. First, the standard form of an observer is obtained by using the Luenberger observable canonical form. Second, the design procedure of a multi-linear functional observer is derived using this standard form. Observers derived using this procedure are generally o flower order than those of Luenberger. Lastly, the procedure presented is illustrated by an example.