  We propose an extension to our monotone and convergent method for the
Monge-Amp\`{e}re equation in dimension $d \geq2$, that incorporates the idea of
filtered schemes. The method combines our original monotone operator with a
more accurate non-monotone modification, using an appropriately chosen filter.
This results in a remarkable improvement of accuracy, but without sacrificing
the convergence to the unique viscosity solution.
