By changing the parameters of corrugations（raidus

equivalent admittance and conical angle） in a special way

We can suppress the harmful modes or produce special high order modes

and improve the performances of horns. Horns are analyzed with their parameters changed continuously or in a broken-line manner

and their enginnering design formulas have been derived. As a practical example

both the theoretical and experimental performances of a complex multimode horn are given

and they are found in satisfactory agreement.