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mkdir $BRANCH
cd $BRANCH
git init
git remote add -t $BRANCH -f origin $REMOTE_REPO
git checkout $BRANCH

oppure
mkdir newrepo.git
cd newrepo.git
git init
git remote add origin file:///path/to/original 
git fetch origin branchiwant:refs/remotes/branchiwant
git checkout -b branchiwant --track origin/branchiwant