We derive an analytical expression for the criticality condition of the fully anisotropic Ising model with next-nearest neighbour interaction. For that behalf a recently published method [H.J.W. Zandvliet, Eur. Phys. Lett. 73 (2006) 747] to calculate the free energy of a boundary between two areas of opposite magnetisation is generalised to systems without reflection symmetry with respect to the boundary line. For the anisotropic triangular model and related special cases without crossing bonds the method provides the exact criticality conditions in polynomial form, which is shown to be a factor of the exactly known criticality condition. The other factor is related to the first one by a reciprocal transformation. For systems with crossing bonds the method is not exact, but it may be useful as a closed form approximation in a wide parameter range.