From Longman Dictionary of Contemporary Englishon no account/not on any accounton no account/not on any accountADVISEused when saying that someone must not, for any reason, do something On no account must you disturb me. → account
Examples from the Corpus
on no account/not on any account• On no account should you attempt this exercise if you're pregnant.• You shouldn't sign the contract unless you are sure you understand it. Not on any account. 