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 up 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.