In this paper, we shall give another proof of the faithfulness of Blass translation (for short, B-translation) of the propositional fragment L1 of Leśniewski's ontology in the modal logic K \it by means of Hintikka formula\rm . And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic PrL (= GL), that is, K + □(□ϕ⊃ϕ)⊃□ϕ. The faithfulness also holds for normal modal logics, e.g., KD, K4, KD4, KB. We shall conclude this paper with the section of some open problems and conjectures.