Improvement of the absorbing boundary conditions for triangle-hexagonal dual cell grids in the time domain method is described in this paper. The magnetic field components, which are evaluated by the electric fields at the circumcenters of the triangle cells, are conformed to Berenger's perfectly matched layer absorbing boundary conditions. The electric field is linearly interpolated by the fields at the vertices. The lower reflection coefficients in the frequency range for the equilateral and non-equilateral triangle cells are demonstrated.