We present a new algorithm for drawing planar graphs on the plane. It can be viewed as a generalization of the algorithm of Chrobak and Payne, which in turn, is based on an algorithm by de Fraysseix, Pach and Pollack. Our algorithm improves the previous ones in that it does not require a preliminary triangulation step; triangulation proves problematic in drawing graphs ``nicely", as it has the tendency to ruin the structure of the input graph. The new algorithm retains the positive features of the previous algorithms: It embeds a graph of $n$ vertices on a grid of size $(2n-4)\times (n-2)$ in linear time. We have implemented the algorithm as part of a software system for drawing graphs nicely.