In the modal µ-calculus, a formula is well-formed if each recursive variable occurs underneath an even number of negations. By means of De Morgan's laws, it is easy to transform any well-formed formula ϕ into an equivalent formula without negations -the negation normal form of ϕ. Moreover, if ϕ is of size n, the negation normal form of ϕ is of the same size O(n). The full modal µ-calculus and the negation normal form fragment are thus equally expressive and concise.In this paper we extend this result to the higher-order modal fixed point logic (HFL), an extension of the modal µ-calculus with higher-order recursive predicate transformers. We present a procedure that converts a formula of size n into an equivalent formula without negations of size O(n 2 ) in the worst case and O(n) when the number of variables of the formula is fixed.