The orthogonality of the members of given orthonormal basis in Hilbert spaces playing the central role in the study of R-duals of frames.In the generalization and extension of the concept R-dual to continuous frames, we need to the definition of continuous orthonormal basis but in available definitions the orthogonality condition is not mentioned and cannot be obtained from the previous assumptions. To solve this problem, we present a new definition. Using this definition, we defined R-dual of continuous Bessel mappings.
