We study the MaxCut problem for graphs $G=(V,E)$. The problem is NP-hard, there are two main approximation algorithms with theoretical guarantees: (1) the Goemans \& Williamson algorithm uses semi-definite programming to provide a 0.878MaxCut approximation (which, if the Unique Games Conjecture is true, is the best that can be done in polynomial time) and (2) Trevisan proposed an algorithm using spectral graph theory from which a 0.614MaxCut approximation can be obtained. We discuss a new approach using a specific quadratic program and prove that its solution can be used to obtain at least a 0.502MaxCut approximation. The algorithm seems to perform well in practice.