Supposing that you had a git server, we can use exist git as your own working bare.

[On your own git server] Create a repo.
Clone an exist git.

$ git clone git@exist-server:exist.git

Make its master branch writable.

$ echo -e "[receive]ntdenyCurrentBranch = ignore" >> exist.git/.git/config

[On your client] Create a branch & make a change.
Clone exist.git as your own git-src, in which you can see the old commits and branch.

$ git clone git@your-server:exist.git
$ cd exist

We create a new branch based on its master.

$ git checkout -b mybranch
$ echo "Add README" > README
$ git add README
$ git commit -m "Add READEME in ROOT"

Since this is our first commit, we should push our branch to origin. Next time you should just type ‘git push’

$ git push origin mybranch

[On your own git server] An update in master.
Let’s get some new commits.

$ git pull

Here we get something like this…


Now we get commit0 and commitA on mybranch, with commit0 and commit1 on branch master.
What we want is something like this.


[On your client] Merge commit1 to mybranch
Way 1.Just merge them from your own git server

$ git pull origin master

Way 2.Pull commit1 to local master, then rebase or merge it to mybranch
Merge:

$ git merge master

Rebase:

$ git rebase master

Final step:

$ git push

There’s a little difference between merge and rebase in history.
Reference:
http://gitbook.liuhui998.com/4_2.html