The invention concerns a sequential liner for a gas turbine combustor, having a sequential liner outer wall spaced apart from a sequential liner inner wall to define a sequential liner cooling channel between the sequential liner outer wall and the sequential liner inner wall. The sequential liner outer wall includes a first face, a first adjacent face and a second adjacent face, the first and second adjacent faces each being adjacent to the first face, the first face of the sequential liner outer wall having a first convective cooling hole adjacent to the first adjacent face and a second convective cooling hole adjacent to the second adjacent face, each convective cooling hole being arranged to direct a convective cooling flow into the sequential liner cooling channel adjacent to each adjacent face. The invention also concerns a method of cooling using the sequential liner and a method of retrofitting a gas turbine.