The Collaborative International Dictionary of English v.0.48:
Perineurium \Per`i*neu"ri*um\, n. [NL., fr. Gr. peri` about + ney^ron a nerve.] (Anat.) The connective tissue sheath which surrounds a bundle of nerve fibers. See Epineurium, and Neurilemma. [1913 Webster]WordNet (r) 3.0 (2006):
perineurium n 1: the sheath of connective tissue that covers a bundle of nerve fibers