We analyse an initial-boundary value problem for the mKdV equation on a finite interval $(0,L)$ by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex $k$-plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at $t=0$ and $x=0,L$. We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...