  In this paper, we give new constructions of Urysohn universal ultrametric
spaces. We first characterize a Urysohn universal ultrametric subspace of the
space of all continuous functions whose images contain the zero, from a
zero-dimensional compact Hausdorff space without isolated points into the space
of non-negative real numbers equipped with the nearly discrete topology. As a
consequence, the whole function space is Urysohn universal, which can be
considered as a non-Archimedean analog of Banach--Mazur theorem. As a more
application, we prove that the space of all continuous pseudo-ultrametrics on a
zero-dimensional compact Hausdorff space with an accumulation point is a
Urysohn universal ultrametric space. This result can be considered as a variant
of Wan's construction of Urysohn universal ultrametric space via the
Gromov--Hausdorff ultrametric space.
