A system for mounting a covering (e.g., a fabric material) upon a frame is constructed from a plurality of elongated frame parts. Each frame part has two mitered ends and a channel formed therein. The related mounting method includes the steps of: (a) using a jig to hold the fabric material against the frame; (b) inserting a plurality of retaining splines within respective channels so as to capture the fabric material within the channels between one retaining spline and a corresponding floor of the channel, whereby a plurality of corner pleats are formed; and (c) using a tool to invert each corner pleat into a corner joint formed between respective adjacent frame parts so as to form an internal fold at each corner of the frame.