Story of La Llorona

Has anyone heard of the story "La Llorona?" I found it in a book, though it
doesn't say which part of Mexico it originated from. Apparently, it is
about a woman who drowns her own children in a river to keep their father
from taking them from her, then cannot get into heaven until she recovers
their souls, crying and wailing as she searches the riverbanks in the night
with her bony fingers. One of those "Golden Arm" spooky stories you tell
children. Anyways, I was wondering if anyone had heard of it and knew where
it originated. I had recently seen a movie on television where one man has
three girlfriends and they find out about it and become very angry. He
starts having frightening visions of La Llorona coming after him, which made
me think it was about a story from Mexico. I soon found the story, but it
does not say which part of Mexico it is from.

Corrine Ardoin