Let $S$ be a compact complex surface with ordinary singularities.
We denote by $\Theta_S$ the sheaf of germs of holomorphic tangent
vector fields on $S$. In this paper we shall give a description
of the cohomology $H^1(S, \Theta_S)$, which is called the
infinitesimal locally trivial deformation space of $S$,
using a 2-cubic hyper-resolution of $S$ in the sense of
F. Guillén, V. Navarro Aznar et al. ([1]). As a by-product,
we shall show that the natural homomorphisim $H^1(S, \Theta_S)\rightarrow
H^1(X, \Theta_X(-\log D_X))$ is injective under some condition,
where $X$ is the (non-singular) normal model of $S$, $D_X$
the inverse image of the double curve $D_S$ of $S$ by the
normalization map $f\colon X\rightarrow S$, and $\Theta_X(-\log D_X)$
the sheaf of germs of logarithmic tangent vector fields along $D_X$ on $X$.
Note that the cohomology $H^1(X, \Theta_X(-\log D_X))$
is nothing but the infinitesimal locally trivial deformation
space of a pair $(X, D_X)$.