A combustion membrane for a gas burner includes a base fabric forming a metal thread braid including multi-fiber warp threads and multi-fiber weft threads transverse to the multi-fiber warp threads. The base fabric is made on a loom and the multi-fiber warp and weft threads each include a bundle of a plurality of metal fibers having a fiber thickness less than 50 micrometers. The combustion membrane also includes a plurality of monofilament metal threads each having a monofilament thickness greater than 100 micrometers, that are directly woven into the base fabric by loom weaving to increase the stiffness of the combustion membrane.