This invention relates to a sheet membrane for repairing a damaged tissue. The membrane includes an isotropic layer of cross-linked biopolymeric fibers in which the fibers are 10 to 1,000 cm in length. This invention also relates to a method of making an isotropic layer of cross-linked biopolymeric fibers. The method includes: (1) coacervating biopolymeric fibers (e.g., collagen-based fibers) having lengths of less than 1 cm dispersed in an aqueous solution to obtain coacervated biopolymeric fibers having lengths of 10 to 1,000 cm; (2) flattening the coacervated biopolymeric fibers into a layer; (3) drying the layer; and (4) cross-linking the biopolymeric.