  It is well-known that each solution of the mKdV equation gives rise, via the
Miura transformation, to a solution of the KdV equation. In this work, we show
that a similar Miura-type transformation exists also for the ``good''
Boussinesq equation. This transformation maps solutions of a second-order
equation to solutions of the fourth-order Boussinesq equation. Just like in the
case of mKdV and KdV, the correspondence exists also at the level of the
underlying Riemann--Hilbert problems and this is in fact how we construct the
new transformation.
