  Young diagrams are fundamental combinatorial objects in representation theory
and algebraic geometry. Many constructions that rely on these objects depend on
variations of a straightening process that expresses a filling of a Young
diagram as a sum of semistandard tableaux subject to certain relations. This
paper solves the long standing open problem of giving a non-iterative formula
for straightening a filling. We apply our formula to give a complete
generalization of a theorem of Gonciulea and Lakshmibai.
