"Not on the books" is a phrase often used to describe an event, transaction, or income that is not officially recorded or documented. This term is commonly used in the business and finance industry, but can also be used in everyday spoken language. Synonyms for "not on the books" include "off the record," "under the table," "unrecorded," "informal," and "unofficial." These words convey the idea of something that is not documented or legitimized by official channels. It is a phrase that is often used when something is being done secretly or outside of legal or ethical boundaries. It is important to be aware of the implications of using these synonyms and to use them appropriately in the right context.