A method and apparatus for chemical mechanical polishing of substrates, and more particularly a method and apparatus related to a carrier had for use in chemical mechanical polishing is provided. In one embodiment the carrier head assembly comprises a base assembly for providing support to the substrate, a flexible membrane mounted on the base assembly having a generally circular central portion with a lower surface that provides a substrate mounting surface, and a plurality of independently pressurizable chambers formed between the base assembly and the flexible membrane, comprising an annular outer chamber and a non-circular inner chamber, is provided.