  V. Bondarenko and Y. Drozd gives a description of all indecomposable objects
in a category of representations of posets, nowadays known as the Bondarenko's
category. This category was essential for V. Bekkert and H. Merklen classify
all indecomposable objects of the derived category of gentle algebras. In view
of this connection with the derived category, which possess a triangulated
structure, and of the fact that in this paper we show that the Bondarenko's
category is not an abelian category, it is reasonable to contemplate the
existence of a triangulated structure for the Bondarenko's category.
  In this paper we introduce a triangulated category structure over a quotient
of Bondarenko's category, which will allow to use the techniques of
triangulated category to study representations of posets.
