Clifford analysis is a higher dimensional function theory offering a refinement of classical
harmonic analysis, which has proven to be an appropriate framework for developing a higher dimensional continuous
wavelet transform theory. In this setting a very specific construction of the wavelets has been established,
encompassing all dimensions at once as opposed to the usual tensorial approaches, and being based on generalizations to
higher dimension of classical orthogonal polynomials on the real line, such as the radial Clifford--Hermite polynomials,
leading to Clifford--Hermite wavelets. More recently, Hermitian Clifford analysis has emerged as a new and successful
branch of Clifford analysis, offering yet a refinement of the orthogonal case. In this new setting a Clifford--Hermite
continuous wavelet transform has already been introduced in earlier work, its norm preserving character however being
expressed in terms of suitably adapted scalar valued
inner products on the respective $L_2$--spaces of signals and of transforms involved. In this contribution we present
an alternative Hermitian Clifford--Hermite wavelet theory with Clifford algebra valued inner products, based on an
orthogonal decomposition of the space of square integral functions, which is obtained by introducing a new Hilbert
transform in the Hermitian setting.