This paper uses the resources of illocutionary logic to provide a new understanding of the Liar Paradox. In the system of illocutionary logic of the paper, denials are irreducible counterparts of assertions; denial does not in every case amount to the same as the assertion of the negation of the statement that is denied. Both a Liar statement, (a) Statement (a) is not true, and the statement which it negates can correctly be denied; neither can correctly be asserted. A Liar statement, more precisely, an attempted Liar statement, fails to fulfill conditions essential to statements, but no linguistic rules are violated by the attempt. Ordinary language, our ordinary practice of using language, is not inconsistent or incoherent because of the Liar. We are committed to deny Liars, but not to accept or assert them. This understanding of the Liar Paradox and its sources cannot be fully accommodated in a conventional logical system, which fails to mark the distinction between sentences/statements and illocutionary acts of accepting, rejecting, and supposing statements.