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Given a pair of biorthogonal multiscaling functions, we present an algorithm for raising their approximation orders to any desired level. Precisely, let 8.x/ and8.x/ be a pair of biorthogonal multiscaling functions of multiplicity r , with approximation orders m andm, respectively. Then for some integer s, we can construct a pair of new biorthogonal multiscaling functions 8 new .x/ = [8 T .x/; r +1 .x/; r +2 .x/; : : : ; r +s .x/] T and8 new .x/ = [8.x/ T ;˜ r +1 .x/;˜ r +2 .x/; : : : ;˜ r +sdoi:10.1017/s1446181100010105 fatcat:g3sswu333rcexkh3aa7lp2q6ri