Recent claims that bent core molecules can exhibit the elusive biaxial nematic phase reveal a molecular structure that differs significantly from the geometry predicted by theory. One proposed reason for this is the large transverse dipole. We have used computer simulations to investigate this using a simple lattice model for a bent core mesogen. We observe that the biaxial nematic to isotropic phase transition is no longer restricted to a single angle. Instead the Landau point splits into a Landau line and this transition can occur for a range of angles. The transition also becomes first order rather than continuous. (c) 2007 Elsevier B.V. All rights reserved.