  Let $\{X_n\}_{n\in\mathbb{N}}$ be a sequence of i.i.d. random variables in
$\mathbb{Z}^d$. Let $S_k=X_1+...+X_k$ and $Y_n(t)$ be the continuous process on
$[0,1]$ for which $Y_n(k/n)=S_k/\sqrt{n}$ $k=1,...,n$ and which is linearly
interpolated elsewhere. The paper gives a generalization of results of Belkin,
\cite{B72} on the weak limit laws of $Y_n(t)$ conditioned to stay away from
some small sets. In particular, it is shown that the diffusive limit of the
random walk meander on $\mathbb Z^d: d\ge 2$ is the Brownian motion.
