We suppose that prior to partitioning a set of experimental units into experimental blocks of size t, each unit is classified with respect to k different binary variables or attributes. The 2k cells of this classification are then used as building blocks to form experimental blocks of t homogeneous experimental units.In our attempt to achieve within-block homogeneity we first order the 2⊃ cells in a sequence so that any two adjacent cells differwith respect to exactly one attribute. The contents of each cell are then partitioned into blocks and, where necessary, units from adjacent cells are combined to form blocks. In the ease of standardized quantitative variables which have been dichotomized at zero, a within-cell partition is based upon an ordering of the experimental units with respect to that particular quantitative variable which changes its sign in the next cell of the sequence.