Assembly line balancing consists of assigning work elements, which are subject to sequencing restrictions, along an assembly line in an optimal manner. The procedure presented in this paper leads to optimal line balances by operation on a matrix of zeros and ones called a “Precedence Matrix.” A nine element problem is used to illustrate the method in detail and comparisons with other procedures are made. Several balances obtained by applying the FORTRAN program appended to the paper to actual and sample problems are also shown.