A chromium-free welding consumable and a method of welding stainless steel to reduce the presence of chromium emissions. The consumable is made from an alloy that reduces the emission of chromium during a welding process, and include predominantly nickel, with between approximately five and twenty five percent by weight copper, up to approximately five percent by weight of palladium, up to approximately ten percent by weight of molybdenum and up to five percent non-copper alloying ingredients. Welding consumables made from the alloy are particularly well-suited for welding austenitic stainless steels, such as type 304 stainless steel. The method involves using chromium-free weld filler material with a stainless steel base material.