In [9 Giraldo , H. , Merklen , H. ( 2009 ). Irreducible morphisms of categories of complexes . Journal of Algebra 321 : 2716 – 2736 .[Crossref], [Web of Science ®] , [Google Scholar]] Giraldo and Merklen studied irreducible morphisms in the categories 𝒞(𝒜) and D−(Λ), where 𝒞(𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and D−(Λ) is the derived category of the bounded above complexes of finite generate left modules, over an Artin algebra Λ. In this work, we continue the study of irreducible morphism having one finite irreducible truncation.