Catalysis of the reaction: UDP-N-acetyl-D-glucosamine + beta-D-mannosyl-R = UDP + 4-(N-acetyl-beta-D-glucosaminyl)-beta-D-mannosyl-R.
UDP-N-acetyl-D-glucosamine:beta-D-mannosyl-glycoprotein 4-beta-N-acetyl-D-glucosaminyltransferase activity