This paper presents an effective and easy-to-implement algorithm to compute orthogonal vanishing points in uncalibrated images of man-made scenes. The main contribution is to estimate the zenith and the horizon line before detecting the vanishing points, using simple properties of the central projection and exploiting accumulations of oriented segments around the horizon. Our method is fast and yields an accuracy comparable, and even better in some cases, to that of state-of-the-art algorithms.