A rotational parameter R_θ has been introduced to complex wavelet transform (CWT). The rotational CWT (RCWT) corresponds to a matrix element 〈ψ|U₂ (θ;μ;k)|F〉in the context of quantum mechanics, where U₂(θ;μ;k) is a two-mode rotational displacing-squeezing operator in the 〈η| representation. Based on this, the Parseval theorem and the inversion formula of RCWT have been proved. The concise proof not only manifestly shows the merit of Dirac's representation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.