The traditional line balancing (LB) problem considers a production line in which stations are arranged consecutively in a line. A balance is determined by grouping tasks into stations while moving forward (or backward) through a precedence network. Recently many production lines are being arranged in a "U-line," as a consequence of the use of just-in-time production principles in many factories. In this paper the U-line LB problem is introduced and modelled, and solution procedures are developed. It more complex than the traditional LB problem because tasks can be grouped by moving forward, backward, or simultaneously in both directions, through the precedence network. We also show how solution techniques developed for the traditional LB problem can be adapted for use with the new problem. Some computational results for well-known problems from the literature are given.