It is proved that a 3-dimensional cubic differential equation has a transitive attractor similar to that of the geometric model of the Lorenz equations. Such an attractor results if a double homoclinic connection of a fixed point with a resonance condition among the eigenvalues is broken in a careful way. This is an interesting variation of a result of M. Rychlik [‘Lorenz attractors through Sil’nikov-type bifurcation. Part I.’ Ergod. Theor. Dyn. Syst., in press].