A method for generating combustion by means of a burner assembly and corresponding burner assembly are disclosed. The burner assembly comprises a refractory block, a fuel supply system and an oxidant supply system. The refractory block defines along one plane P1 at least one fuel passageway extending from a fuel inlet port to a fuel outlet port, and along a second plane P2 at least one oxidant passageway extending from an oxidant inlet port to an oxidant outlet port, said first and second planes intersecting along a line that is beyond said outlet ports, said oxidant supply system comprising a pair of oxidant supply means, an inlet of the inner oxidant supply means being connected to a source of a first oxidant having a first oxygen concentration and an inlet of the concentric outer oxidant supply means being connected to a source of a second oxidant having a second oxygen concentration, the method having improved flexibility in oxygen concentration in the oxidant.