  We study the traditional backward Euler method for $m$-dimensional stochastic
differential equations driven by fractional Brownian motion with Hurst
parameter $H > 1/2$ whose drift coefficient satisfies the one-sided Lipschitz
condition. The backward Euler scheme is proved to be of order $1$ and this rate
is optimal by showing the asymptotic error distribution result. Two numerical
experiments are performed to validate our claims about the optimality of the
rate of convergence.
