  We propose a new algorithm to generate a fractional Brownian motion, with a
given Hurst parameter, 1/2<H<1 using the correlated Bernoulli random variables
with parameter p; having a certain density. This density is constructed using
the link between the correlation of multivariate Gaussian random variables and
the correlation of their dichotomized binary variables and the relation between
the correlation coefficient and the persistence parameter. We prove that the
normalized sum of trajectories of this proposed random walk yields a Gaussian
process whose scaling limit is the desired fractional Brownian motion with the
given Hurst parameter, 1/2<H<1
