Consider a non specific organization that has been using a project management methodology based on decision stages, basic planning and execution tools to deliver quality projects but has still been missing the planned schedule in a higher rate than desirable. Going beyond the resources offered by consolidated project management methodologies to improve these results, the purpose of this paper is to apply TRIZ (Theory of Inventive Problem Solving) to the referred situation and check if it can support the search for additional alternatives to solve the hidden contradiction that is how to accelerate projects without compromising the delivered systems quality.