  The square tight-binding model in a magnetic field leads to the
almost-Mathieu operator which, for rational fields, reduces to a $q\times q$
matrix depending on the components $\mu$, $\nu$ of the wave vector in the
magnetic Brillouinzone. We calculate the corresponding Green's function without
explicit knowledge of eigenvalues and eigenfunctions and obtain analytical
expressions for the diagonal and the first off-diagonal elements; the results
which are consistent with the zero magnetic field case can be used to calculate
several quantities of physical interest (e. g. the density of states over the
entire spectrum, impurity levels in a magnetic field).
