A first stage vane arrangement having an array of first stage vanes and an array of frame segments and method for cooling frame segments of the first vane arrangement of a gas turbine are disclosed. The frame segments are designed for axially receiving aft ends of a combustor transition pieces. The first stage vanes include extended vanes, each vane having a leading section, a trailing edge, and an airfoil extending between an outer platform and an inner platform. The frame segments having an I-beam with an upper horizontal element, a lower horizontal element, and a vertical web. The vertical web having a downstream face facing towards a first stage of a turbine when installed in a gas turbine. The downstream face of the vertical web of at least one of the frame segments overlaps, at least partially, the leading section of at least one of the extended vanes.