A proposal for the matrix model formulation of the M-theory on a space with a
boundary is given. A general machinery for modding out a symmetry in M(atrix)
theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The
construction causes the elements of matrices to be equivalent to real numbers
or quaternions and the symmetry U(2N) of the original model is reduced to O(2N)
or USp(2N)=U(N,H). We also show that membranes end on the boundary of the
spacetime correctly in this construction.