Yes. The modern technique of pterygium removal is called pterygium excision with conjunctival autografting (PECG). This is an out-patient procedure and takes about 15-20 minutes.
During the procedure, you are awake, but you are given medicine that will make you relaxed so you do not feel any pain, and often you do not remember the procedure. Dr. Levinson will remove the pterygium in the operating room, and place a conjunctival autograft in its place.