  We study the plus and minus type discrete mKdV equation. Some different
symmetry conditions associated with two Lax pairs are introduced to derive the
matrix Riemann-Hilbert problem with zero. By virtue of regularization of the
Riemann-Hilbert problem, we obtain the complex and real solution to the plus
type discrete mKdV equation respectively. Under the gauge transformation
between the plus and minus type, the solutions of minus type can be obtained in
terms of the given plus ones.
