The Bethe-Salpeter equation for three scalar bosons, with zero-range interaction, has been solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators were handled by standard analytical and numerical methods, without using any ansatz for the Bethe-Salpeter amplitude. Some of the results for the binding energies and transverse amplitudes are discussed here, and also compared with the corresponding results calculated in Euclidean space. A reasonable agreement between the calculations has been obtained.