This research presents an interactive procedure for solving Multiple Objective Integer Linear Programming Problems (MOILP). The procedure uses preference information extracted during the interactive steps of the procedure to help the decision-maker (DM) find a preferred integer solution. The scenario considered here assumes that the DM cannot provide a quantitative specification of his (her) preferences in the form of a utility function. The demands imposed by the procedure upon the DM consist of requesting from him (her) the indication of the least preferred solution from a reduced set of candidate efficient solutions presented to him (her) for examination at each interaction. These candidate solutions are generated by the procedure utilizing a software package that solves single objective integer linear programming problems. In the last interaction, the DM is requested to select the most preferred solution from the reduced set that contains those solutions that are more attractive to him. A test problem is presented and solved following the indications of the procedure.