$ git checkout --orphan NEWBRANCH
$ git rm -rf .

--orphan creates a new branch, but it starts without any commit. After running the above command you are on a new branch "NEWBRANCH", and the first commit you create from this state will start a new history without any ancestry.

You can then start adding files and commit them and they will live in their own branch. If you take a look at the log, you will see that it is isolated from the original log.