Latin squares have been widely used to design an experiment where the blocking factors and treatment factors are of the same levels.For some experiments,the size of blocks may be less than the number of treatments.Since not all of the treatments can be compared within each block,a new class of designs called balanced incomplete Latin squares (BILS) is proposed to deal with such experiments.A general method for constructing BILS is proposed by an intelligent selection of certain cells from a complete Latin square via orthogonal Latin squares.The optimality of the proposed BILS designs is investigated.It is shown that the proposed transversal BILS designs are asymptotically optimal for all the row,column and treatment effects.The relative effciencies of a delete-one-transversal BILS design with respect to the optimal designs for both cases are also derived; it is shown to be close to 100%,as the order becomes large.