It is widely-accepted that Descartes is a substance dualist, i.e. that he holds that there are two and only two kinds of finite substance – mind and body. However, several scholars have argued that Descartes is a substance trialist, where the third kind of substance he admits is the substantial union of a mind and a body, the human being. In this paper, I argue against the trialist interpretation of Descartes. First, I show that the strongest evidence for trialism, based on Descartes' discussion of so-called incomplete substances, is highly inconclusive. Second, I show that a kind of unity (‘unity of nature’), which is had by all and only substances, is not had by human beings. The fact that the proper parts of a human being, namely a mind and a body, are of different natures entails that what they compose has at most a ‘unity of composition’. And a thing cannot be a substance in virtue of having a unity of composition. Therefore, Cartesian human beings are not substances.