How to remove a file from GIT tracking?

Pro git rm and .gitignor know about git rebase, but it has not yet managed to solve the case.

So. What is the question?

You must delete the file or folder from the tracking (e.g. the master branch) like this would happen in a team
git rm --cache filename
the one exception to the other members when they do
git pull origin master
the file filename was not deleted.
It is very desirable that GIT had forgotten about the fact that this file has ever tracked, in other words to Delta that file is not ranked in the repository and had no references.

I believe that there needs rebase git change commit when the file was added to repository, but until something obvious result is not received.