  In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills
(SYM) theory and deform it by a mass parameter M with keeping all supercharges.
We further add another mass parameter m in a manner to respect two of the eight
supercharges and put the deformed theory on a two-dimensional square lattice,
on which the two supercharges are exactly preserved. The flat directions of
scalar fields are stabilized due to the mass deformations, which gives discrete
minima representing fuzzy spheres. We show in the perturbation theory that the
lattice continuum limit can be taken without any fine tuning. Around the
trivial minimum, this lattice theory serves as a non-perturbative definition of
two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice
theory realizes four-dimensional N = 2 U(k) SYM on R^2 x (Fuzzy R^2) around the
minimum of k-coincident fuzzy spheres.
