A unital C*-algebra A is said to have cancellation of projections if the semigroup D(A) of Murray- von Neumann equivalence classes of projections in matrices over A is cancellative. It has long been known that stable rank one implies cancellation for any A, and some partial converses have been established. In this paper it is proved that cancellation does not imply stable rank one for simple, stably finite C*-algebras. i=1 biai =1 is dense in A n .I f no suchn exists, then one says that the stable rank of A is infinite. In the case of a commutative C*-algebra, the stable rank is proportional to the covering dimension of the spectrum; stable rank may be viewed as a kind of non-commutative dimension. Given a unital C*-algebra A ,l etD(A) be the Abelian semigroup obtained by endowing the set of Murray-von Neumann equivalence classes of projections in matrix algebras over A with the addition operation coming from direct sums. The algebra A is said to have cancellation of projections if x + y = x + z implies that y = z for any x, y, z ∈ D(A). Shortly after the appearance of Rieffel's paper, Blackadar showed that stable rank one implies cancellation of projections (1). He also established a partial converse: if a C*-algebra of real rank zero has cancellation of projections, then it has stable rank one. The relationship between cancellation and stable rank for general simple, stably finite C*-algebras, however, remained unclear. The lack of examples of simple, stably finite C*-algebras with non-minimal stable rank was a serious obstacle. Villadsen provided the first such examples in (7), but determining whether his examples had cancellation of projections was all but impossible, due to their extremely complicated K-theory. Recently, the author has been able to apply Villadsen's techniques to construct simple, stably finite C*-algebras with non-minimal stable rank and cyclic K0-groups. These algebras constitute the first simple, nuclear and stably finite counterexamples to Elliott's classification conjecture for nuclear C*-algebras (2, 6). In this paper we study one such algebra in order to prove our main result.