  Let {\cal T} be a triangulated category, {\cal A} a full subcategory of {\cal
T} and {\cal X} a functorially finite subcategory of {\cal A}. If {\cal A} has
the properties that any {\cal X}-monomorphism of {\cal A} has a cone and any
{\cal X}-epimorphism has a cocone. Then the subfactor category {\cal A/[X]}
admits a pretriangulated structure in the sense of [BR]. Moreover the above
pretriangulated category {\cal A/[X]} with ({\cal X},{\cal X}[1]) = 0 becomes a
triangulated category if and only if ({\cal A},{\cal A}) forms an {\cal
X}-mutation pair and {\cal A} is closed under extensions.
