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Balinese media are reporting that Temson Junior Simeki (23) disappeared while trying to save his German girlfriend, named as Leonie Hafke (20).
Mr Simeki was among three people taking photos at the Angel Billabong tourist spot when the wave hit yesterday morning (local time), AP reports.
Ms Hafke was knocked into the sea and Mr Simeki, from Auckland, jumped in to save her.
However, he disappeared and Ms Hafke was rescued by an Australian snorkeller.
A search for Mr Simeki was due to resume this morning.
A spokeswoman for the Ministry of Foreign Affairs and Trade said it was looking into the Mr Simeki's disappearance.