It is a classical result that there is no compactly supported, symmetric, orthogonal univariate scalar wavelet. In this paper, the author aims to obtain multi-wavelets with several good properties. That is, the multi-wavelets are compactly supported, symmetric, orthogonal and have suitable vanishing moments. Firstly, we point out that the orthogonality and symmetry of the multi-wavelets can be obtained if the filter banks are constructed by matrix factorization. Secondly, it is presented how the choices of 2-th real orthogonal matrices matters in the construction. In the end, this paper discusses how the parameters are chosen so that the multi-wavelets will have suitable vanishing moments.