We’ve been following Twitter co-founder Jack Dorsey’s new startup, Square Inc. for awhile now, and most recently we have seen his company grow in size to reach over 2 billion users.

The service is currently processing $6 billion in mobile payments annually and is accepted at over 20,000 retail outlets and is growing everyday.

Now the company is introducing a loyalty and rewards system, which allows merchants to create digital punch cards for users, rewarding them for their first visit and continued patronage.

It’s very simple to use. Consumers will get a push card for their Pay with Square Mobile App (now available for Android) for each participating retailer and can keep track of their progress through the cards.

Using the method, Square retailers can gain access to better analytics on sales, and customers can get incentives or free merchandise. All of the refinements represent increased value for merchants and easier usability for customers.

Since the launch of Square Register, the mobile app for iPad square payers, users have been five times more active on a weekly basis and have spent twice as much money using the service.

This latest introduction from Square might be working in the right direction, but they still face major competition from their largest competitor, PayPal. Aside from partnering with fifteen nationwide retailers on an exclusive payment system, PayPal has also just partnered with Comcast Cable and TiVo to introduce payments from a conventional television set utilizing viewer’s remote controls.

In my mind, there’s room for both services in the marketplace, but clearly PayPal has the advantage. They’re well-established, require no addition equipment to utilize, and offer the security of the PayPal brand name. We’ll see what happens as Square continues to adapt and offer new features.