Workers in a bucket brigade production system perform unproductive travel when they walk to get more work from their colleagues. We introduce a new design of bucket brigades to reduce unproductive travel. Under the new design, each worker works on one side of an aisle when he proceeds in one direction and works on the other side when he proceeds in the reverse direction. We propose simple rules for workers to share work under the new design and find a sufficient condition for the system to self-balance. Numerical examples suggest that the improvement in throughput by the new design can be as large as 30%. Even with a 20% reduction in labor, the new design can still increase throughput by 7%.