Three impotant results are given on normalized tight frame super-wavelets in the article. Firstly, A normalized tight frame super-wavelets of length in the space can be extended to a super-wavelets of length in the bigger space .That is a normalized tight super-wavelets frame in the space is extendable to an orthonormal basis in the bigger space . So the relationship between parseval super-wavelets and super-wavelets is found. Secondly, the equivalence of the normalized tight frame super-wavelets are studied by means of the unitary equivalence.The m-tuple remainly forms a normalized tight frame super-wavelets ,when the final component of normalized tight frame super-wavelets is unitarily replaced by a normalized tight frame wavelet. Finally, the conditions of the normalized tight frame super-wavelets are improved. A sufficent condition on a normalized tight frame super-wavelets is given by using space theory. The three results are proofed by using functional analysis. These results function as the important theory basis for the signal processing in the space .