The purpose of this note is to show that the completeness of a set of complex exponentials {e'x"'} in L2(—7r,w) is preserved whenever the \n are subjected to a suitable "lifting". There is an extensive literature on the completeness of sets of complex exponentials {e'x"') (see, for example, [l]-[8], and the references therein). In this note, we show that completeness is preserved in L?(—77,77) ...