An extended directed triple system of the order v with a idempo-tent element (EDTS(v, a)) is a collection of triples of the type [x, y, [x, y, x] or [x, x] chosen from a v-set such that every ordered pair (not necessarily distinct) belongs to only one triple and there are a triples of the type {x, x, x}. If such a design with parameters v and a exist, then they will have b_(v,a) blocks, where b_(v,a) = (v~2+ 2a)/3. A necessary and sufficient condition for the existence of EDTS(v, 0) and EDTS(v, 1) are v≡ 0 (mod 3) and v ≡ 0 (mod 3), respectively. In this paper, we have constructed two EDTS(v, a)'s such that the number of common triples is in the set {0, 1, 2,...,b_(v,a)-2, b_(v,a)}, for a = 0, 1.
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