  We develop a formalism for performing real space renormalization group
transformations of the "decimation type" using perturbation theory. The type of
transformations beyond $d=1$ is nontrivial even for free theories. We check the
formalism on solvable case of $O(N)$ symmetric Heisenberg chain.
  The transformation is particularly useful to study asymptotically free
theories. Results for one class of such models, the d=2 O(N) symmetric $\sigma$
models ($N\ge 3$) for decimation with scale factor $\eta=2$ (when quarter of
the points is left) are given as an example.
