In E. G. Effros’s paper [4] given at the 1980 Kingston Conference of the American Mathematical Society, he stated that "an example of a finite but not stably finite C ∗ {C^*} -algebra has yet to be found." This paper seeks to give an example of such an algebra by using a simple application of the duality between K K and Ext-theory arising from the work of Brown, Douglas and Fillmore (see, for example, [2 and 3]).