  We introduce new Gaussian proposals to improve the efficiency of the standard
Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used
for the sampling from a target distribution in large dimension $d$. The
improved complexity is $\mathcal{O}(d^{1/5})$ compared to the complexity
$\mathcal{O}(d^{1/3})$ of the standard approach. We prove an asymptotic
diffusion limit theorem and show that the relative efficiency of the algorithm
can be characterised by its overall acceptance rate (with asymptotical value
0.704), independently of the target distribution. Numerical experiments confirm
our theoretical findings.
