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[SomeRando]

Is there an exclusion period ?

Not according to the T&Cs or the people at OzBargain although some reports say it depends on how many other Citi/NAB backed cards you've had recently and should wait a few months before applying again. Some people reported being approved within days of closing the card though so YMMV.

Personally, I closed the card late March and applied again earlier this month. I was instantly rejected before being able to upload docs or input any information. Other Ozbargainers reported no credit check was done when this happened to them although a credit check appeared on my credit file about a week later.