This paper discusses the existence of a competitive equilibrium when the assumption of perfect divisibility is not fulfilled for all the goods involved in the economy; we limit ourselves to the case of a pure exchange economy with a finite number of traders. Section 2 is devoted to the proof of an existence theorem when assuming that only two goods are exchanged in the economy; in Section 3 we build a counterexample to show the restrictive nature of the assumptions one has to make in order to generalize the above theorem.