A non-contact seal assembly for sealing a gap between relatively rotatable components in a gas turbine engine is presented. The non-contact seal assembly includes a primary seal having a radially movable seal shoe, a mid-plate, an aft secondary seal radially movable along with the seal shoe, a forward secondary seal and a U-shaped seal carrier for holding the components together using pins. The seal shoe includes a plurality of seal shoe segments. The aft secondary seal includes a plurality of aft secondary seal segments. Each aft secondary seal segment is attached to each seal shoe segment. Each aft secondary seal segment includes at least a notch at outer radial side to receive the pin for accommodating radial movement of the seal shoe segment.