$ git clone git@github.com:org/myrepo-original myrepo-new
$ cd myrepo-new
$ git remote set-url origin git@github.com:org/myrepo-new
$ git push origin master

$ git remote add cloned git@github.com:org/myrepo-new

$ git remote -v

origin  git@github.com:org/myrepo-original (fetch)
origin  git@github.com:org/myrepo-original (push)
cloned  git@github.com:org/myrepo-new (fetch)
cloned  git@github.com:org/myrepo-new (push)

$ cd myrepo-original
$ git checkout master
$ git checkout -b master-original
$ git push cloned master-original