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A method is presented that combines the low-frequency accuracy of tree-loop decomposition with higher order basis functions to achieve an electric field integral equation based method of moments that is accurate over a wide band of frequencies. In general, the use of higher order divergence-conforming bases introduces more solenoidal degrees of freedom than the standard Rao-Wilton-Glisson (zeroth-order) bases. These solenoidal degrees of freedom are counted and identified, and an efficient method to construct the required higher order loops is presented. Numerical results demonstrate that the technique allows the use of a single mesh to acquire scattering results over a wide band of frequencies using arbitrary order basis functions.