The notion of isotropic submanifolds of an arbitrary Riemannian manifold was first introduced by B. O'Neill. In this paper, we study $n$-dimensional, totally real, isotropic submanifolds of $CP^n(4)$. These submanifolds have been previously studied by H. Naitoh, S. Montiel and F. Urbano under the additional assumption that $M$ is complete. Here we prove some local classification theorems for totally real isotropic submanifolds of the complex projective space.