Remove file from git history

$ git rm --cached giant_file
# Stage our giant file for removal, but leave it on disk

Commit this change using --amend -CHEAD:

$ git commit --amend -CHEAD
# Amend the previous commit with your change
# Simply making a new commit won't work, as you need
# to remove the file from the unpushed history as well

Push your commits to GitHub:

$ git push
# Push our rewritten, smaller commit