  In this work we introduce correlated random walks on $\Z$. When picking
suitably at random the coefficient of correlation, and taking the average over
a large number of walks, we obtain a discrete Gaussian process, whose scaling
limit is the fractional Brownian motion. We have to use two radically different
models for both cases ${1\over2}\leq H<1$ and $0<H<{1\over2}$. This result
provides an algorithm for the simulation of the fractional Brownian motion,
which appears to be quite efficient.
