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Traditionally, in the electromagnetic frequency domain surface integral equations only the (rotated) tangential components of the fields are used as unknowns and are discretized with divergence-conforming basis function such as the RWGpsilas. In the current and charge integral equation (CCIE) formulations the normal components of the fields, were introduced as unknowns, too. The CCIE formulations are better balanced and have better iterative convergence but are also more complicated to implement. In this presentation both the tangential and the normal components of the fields are discretized element-wise with non-conforming fully orthogonal higher order basis funtion.The use of the orthogonal higher order bases not only gives more accurate results in singular cases, allows to use larger elements and gives better iterative convergences, but also simplifies the implementation of the surface integral equations. Three basic surface integral equations, similar to the traditional EFIE, MFIE, and CFIE, are derived from Picard's extended Maxwell system.