  A method is proposed for exactly calculating the partition function of a
rectangular Ising lattice with the presence of a uniform external field. This
approach is based on the method of the transfer matrix developed about seventy
years ago for the rectangular Ising model in the absence of external field. The
basis for the vector space is chosen as the eigenvectors of the diagonal part
of the transfer matrix. The matrix elements for the non-diagonal part can be
calculated very easily. Then the partition function and thermodynamical
quantities can be evaluated. The limit of infinite lattice is discussed.
