A balanced incomplete block design (BIBD) B [ k , λ ; υ ] is an arrangement of υ elements in blocks of k elements each, such that every pair of elements is contained in exactly λ blocks. A BIBD B [ k , 1 ; υ ] is called resolvable if the blocks can be petitioned into ( υ - 1 ) / ( k - 1 ) families each consisting of υ / k mutually disjoint blocks. Ray-Chaudhuri and Wilson [8] proved the existence of resolvable BIBD's B [ 3 , 1 ; υ ] for every υ ≡ 3 (mod 6). In addition to this result the existence is proved here of resolvable BIBD's B [ 4 , 1 , υ ] for every υ ≡ 4 (mod 12).