GO:0003830:   beta-1,4-mannosylglycoprotein 4-beta-N-acetylglucosaminyltransferase activity
Catalysis of the reaction: UDP-N-acetyl-D-glucosamine + beta-D-mannosyl-R = UDP + 4-(N-acetyl-beta-D-glucosaminyl)-beta-D-mannosyl-R.