Let $\displaystyle X_n $ be a martingale. Show that $\displaystyle Cov ( X_i-X_{i-1}, X_j-X_{j-1})=0 $

So using the covariance formula, I know that $\displaystyle Cov ( X_i-X_{i-1}, X_j-X_{j-1})=E[(X_i-X_{i-1})(X_j-X_{j-1})]-E[X_i-X_{i-1}]E[X_j-X_{j-1}] $

Now I know that I must use the property of martingale in which $\displaystyle E[X_{i+1}|X_i] = X_i $, but how should I mix that property in this problem? Should I take the double expectation on it? Thanks.