The paper studies the unattainability of certain closed-loop pole positions in single-input multi-output systems with constant output feedback. It is shown that there are two classes of unattainable pole positions : those which are unattainable individually and those which are unattainable simultaneously. The individually unattainable pole positions are identified as the locations of the common zeros of the open-loop system, and a set of simultaneously unattainable pole positions results in linearly dependent rows in a certain matrix. Illustrative numerical examples are given.