We present a method for the construction of compactly supported $left ( begin{array}{lll} 1 & 0 & -1\ 1 & 1 & 0 \ 1 & 0 & 1\ end{array} right )$-wavelets under a mild condition. Wavelets inherit the symmetry of the corresponding scaling function and satisfies the vanishing moment condition originating in the symbols of the scaling function. As an application, an example is provided.
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