One of the simplest methods to construct a 3D city model is to extrude building footprints, to obtain "block-shaped" buildings. While the method is well-known and easy to implement, if the topological relationships between the footprints are not taken into account, the resulting city models will not necessarily be topologically consistent. As a result, the model will be of little use for most applications, besides visualisation that is. In this paper, we present a new extrusion algorithm to construct topologically correct 3D city models. It is conceptually simple and permits us to create city models in different formats (e.g. CityGML). We have implemented the algorithm, tested it for the creation of the model of our university campus and validated it by constructing the constrained Delaunay tetrahedralization.