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We take the manifestly gauge invariant exact renormalisation group previouslyused to compute the one-loop beta function in SU(N) Yang-Mills without gaugefixing, and generalise it so that it can be renormalised straightforwardly atany loop order. The diagrammatic computational method is developed to cope withgeneral group theory structures, and new methods are introduced to increase itspower, so that much more can be done simply by manipulating diagrams. The newmethods allow the standard two-loop beta function coefficient for SU(N)Yang-Mills to be computed, for the first time without fixing the gauge orspecifying the details of the regularisation scheme.Comment: 91 pages, 58 figure

A generalised manifestly gauge invariant exact renormalisation group for SU(N) Yang–Mills