M. Matsumoto and R. Miron [2]1) constructed an orthonormal frame for an n-dimensional Finsler space and the frame was called 'Miron frame'. T. N. Pandey and D. K. Diwedi [3] and the present authors [4] studied four-dimensional Finsler spaces in terms of scalars. In the present paper, we study a four-dimensional Berwald space with vanishing h-connection vector k(subscript i).