  We analyse an initial-boundary value problem for the mKdV equation on a
finite interval by expressing the solution in terms of the solution of an
associated matrix Riemann-Hilbert problem in the complex $k$-plane. This
Riemann-Hilbert problem has explicit $(x,t)$-dependence and it involves certain
functions of $k$ referred to as ``spectral functions''. Some of these functions
are defined in terms of the initial condition $q(x,0)=q_0(x)$, while the
remaining spectral functions are defined in terms of two sets of boundary
values. We show that the spectral functions satisfy an algebraic ``global
relation'' that characterize the boundary values in spectral terms.
