We use chain complexes and the algebraic theory of surgery to combine the first and second order knot concordance obstructions of Cochran, Orr and Teichner into a single stage obstruction group. The concordance of high dimensional knots is understood algebraically. The Seifert form obstruction of Levine (1969) distinguishes high dimensional knots S^n in S^{n+2}, for n > 1, up to concordance. The Seifert form also partially distinguishes knots S^1 in S^3. However, in the low dimensional case, this is just the first order obstruction, since in dimensions three and four the fundamental group plays a much greater role. In 2000 Cochran, Orr and Teichner defined an infinite filtration of the knot concordance group. Their second order obstruction theory depends on a choice in the vanishing of the first order obstructions. We define a single obstruction which does not depend on choices.