Abstract: Let TX be the full transformation semigroup on a nonempty set X, E be a nontrivial equivalence relation on Xand R be a cross-section of X/E, then T_E(X,R)=f∈TX:∀x,y∈X,(x,y)∈E ⇒(f(x),f(y))∈E and f(R)⊆Ris a subsemigroup of T、X. By constructing suitable mappings, all the left compatible elements were described in the transformation semigroup T_E(X,R) endowed with the natural partial order and a necessary and sufficient condition for these elements was given