There are a small number of supplies that are Input-taxed. If you make an input-taxed supply, you cannot charge GST but you cannot claim back any of your GST paid.

Input-taxed supplies include:

[list unordered]
Financial supplies
Residential premises for rent
Sales of residential premises (but not new homes)
food at school tuckshops (optional);
fundraising activities of charities (optional)
certain transactions involving precious metals
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When a supply is both a GST-free supply and an input-taxed supply, it is treated as the former.