  For a given symmetric refinable mask obeying the sum rule of order $n$, an
explicit method is suggested for the construction of mutually symmetric almost
frame-like wavelet system providing approximation order $n$. A transformation
based on the lifting scheme is described that allows to improve almost
frame-like wavelets to dual wavelet frames and preserve other properties. A
direct method for the construction of dual wavelet frames providing
approximation order $n$ and mutual symmetry properties is also discussed. For
an abelian symmetry group $H$, a technique providing the $H$-symmetry property
for each wavelet function is given for the above three methods.
