How to duplicate a git repository? (without forking)

I have two repositories, and I need to copy whole of one onto the other empty one which has different access levels from the first one. The copy and the mother repository should not be linked together.

I am new to git and it would be awesome if someone could help me with this.

See https://help.github.com/articles/duplicating-a-repository

Short version:

In order to make an exact duplicate, you need to perform both a bare-clone and a mirror-push:

mkdir foo; cd foo 
# move to a scratch dir

git clone --bare https://github.com/exampleuser/old-repository.git
# Make a bare clone of the repository

cd old-repository.git
git push --mirror https://github.com/exampleuser/new-repository.git
# Mirror-push to the new repository

cd ..
rm -rf old-repository.git  
# Remove our temporary local repository

NOTE: the above will work fine with any remote git repo, the instructions are not specific to github

The above creates a new remote copy of the repo. Then clone it down to your working machine.

You can also use git-copy.

Install it with Gem,

gem install git-copy

Then

git copy https://github.com/exampleuser/old-repository.git \
    https://github.com/exampleuser/new-repository.git

If you are copying to GitHub, you may use the GitHub Importer to do that for you. The original repo can even be from other version control systems.