Let L(H) denote the algebra of operators on a complex infinite dimensional Hilbert space H. For A, B ∈ L(H), the generalized derivation δ A,B and the elementary operator δ A,B are defined by δ A,B(X)=AX-XB and δ A,B}(X)=AXB-X for all X\in L(H). In this paper, we exhibit pairs $(A,B)$ of operators such that the range-kernel orthogonality of δ A,B}$ holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of Δ A,B with respect to the wider class of unitarily invariant norms on L(H).