The problem of placing poles in linear multidimensional systems using a feedback matrix of unlimited rank is considered. The effect of output feedback of indefinite rank of the characteristic polynomial of a system with several variables is studied. The results are then used to obtain a recurrent pole placement algorithm without any restrictions on the rank of the output feedback matrix used. The algorithm is based on the pseudo-inverse concept of obtaining solutions to systems of linear equations using the least squares method and is computationally efficient.