Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.
