  We consider the H\"older continuity for the Dirichlet problem at the
boundary. Almgren introduced the multivalued; Q-valued functions for studying
regularity of minimal surfaces in higher codimension. The H\"older continuity
in the interior for Dirichlet minimizers is an outcome of Almgren's original
theory, to which C. De Lellis and E.N. Spadaro's work have given a simpler
alternative approach. We extend the H\"older regularity for Dirichlet
minimizing Q-valued functions up to the boundary assuming enough regularity of
the domain and H\"older regularity of the boundary data with exponent >1/2.
