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Scheme for teleporting an unknown single-qubit photonic state is revisited.With the help of quantum nonde-molition measurements, the scheme now can be achieved in an almost deterministic way.The weak-cross-Kerr-nonlinearities-based quantum nondemolition measurement acts as an entangler as well as the Bell-state analyzer,and thus plays a similar role as the CNOT gate in the teleportation process.This improvement makes the present scheme more efficient than the schemes using nonunitary projective measurements and feasible with the current experimental technology.