Focus on the customer and document the system/business model that takes place and where your team members fit into it.  Create a common understanding that the puzzle relies on all people working as a team and discuss the impact of a smooth working team vs. a dysfunctional one.  Establish common and individual goals, share them with one another and have regular meetings to evaluate what is working and where improvement needs to take place.  Encourage team members to champion their own improvement plans.

Establish your department's culture.  Answer the questions "What can others in our company expect from us?" What can customers expect from us?"  Document bullet points as answers to these questions.  Train your team to make these bullets a reality.  Inform the rest of the organization of what they can expect from your team.  Post signs if you have to, spreading the word on your team's expectations. 

For more information on how to influence a team culture in your department.  Read the following article: Seven Steps to Improving Your Department’s Culture