We present a new notion of basis that is able to generate the repeated motifs (possibly exponential in number) that appear at least twice with don't care symbols in a string of length n over an alphabet . Our basis has some interesting features such as being (a) a subset of the previously de ned bases, (b) truly linear as its motifs are less than n in number and appear in the string for a total of 2n times at most; (c) symmetric as the basis of the reversed string is the reverse of the basis; (d) computable in polynomial time, namely, in O(n log n log jj) time.