Unit Commitment is an important problem faced by independent system operators and vertically integrated utilities. The problem is to minimize the total commitment and dispatch cost by committing appropriate units while satisfying demand and other constraints. It is usually formulated as a Mixed Integer Linear Programming (MILP) problem, and is NP hard. To obtain high quality solutions within specified amounts of time, most research focuses on solution methodology, and very limited results have been reported on problem formulation. However, it is critically important since if constraints directly delineate the convex hull of an MILP problem, then the problem can be directly solved by linear programming. Tightening formulation, however, is difficult with no systematic approach to be found in the literature. In this paper, a systematic approach based on a novel integration of "constraint-and-vertex conversion" and "vertex projection" processes is developed. The focus is on single units assuming system-wide constraints have been relaxed. Innovative aspects also include the elimination of dependence on initial conditions, and the handling of units with different sets of parameters. Numerical simulation demonstrates great potential for tightening complicated MILP problems.