Improved algorithms are presented to design linear phase digital FIR filters with coefficients of +1,0,-1 only followed by a multiple integrator. It has been shown that the existing linear phase filter design concept for the single integrator(or, accumulator)case can be extended to the case of the multiple integrator. Linear phase conditions for the multiple integrators are summarized. Filter design methods with double or triple integrator are exploited in datail and its computer simulation results are presented to deduce the advantages of multiple integrator to the single integrator.