Every polyhedral simple closed curve in S3 bounds an orientable surface [2]; that is, if k is a knot, then there exists an orientable surface S such that D(S) = k. The minimal genus of all such spanning surfaces is the genus of the knot and a minimal spanning surface is a spanning surface with minimal genus. For the Neuwirth-Stallings [4, 5] knots, it is known that such a minimal surface is unique in the sense that there is a space homeomorphism throwing one minimal surface to any other. The important property here is that the commutator subgroup of the knot group is finitely generated and, hence, free [4]. Stallings then shows that S3 k fibers over S' with fiber a minimal spanning surface of k. Such a fibration can then be used to show the uniqueness of the minimal spanning surface. Hale Trotter, in a letter to C. D. Feustel, indicates that there is an example of a knot with two different minimal surfaces. His example depends heavily on the existence of non-invertible knots [6]. Trotter's example has the property that S3 S1 is homeomorphic to S3 S2. The purpose of this note is to construct a knot k with two minimal spanning surfaces, SI and S2, such that S3 Si are not homeomorphic. The proof actually shows that Z1(S3 Si) are not isomorphic. The author is indebted to Professor C. B. Schaufele, Dr. C. D. Feustel, and Mr. A. C. Connor for helpful conversations.