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This paper investigated the existence of splitting balanced incomplete block designs with blck size 2 ×k.The necessary conditions for such a design are λ(v-1)≡0(mod k),and λv(v-1 )≡0 (mod 2k 2). It will show that the above necessary conditions are also sufficient for k = 3 with the definite exception(v,λ)= (10,1) and with several possible exceptions.