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By incorporating the flavor-dependent quark-antiquark annihilation amplitudeinto the mass-squared matrix describing the mixing of the isoscalar states of ameson nonet, the new version of Schwinger's nonet mass formula which holds witha high accuracy for the $0^{-+}$, $1^{--}$, $2^{++}$, $2^{-+}$ and $3^{--}$nonets is derived and the mixing angle of isoscalar octet-singlet for thesenonets is obtained. In particular, the mixing angle of isoscalar octet-singletfor pseudoscalar nonet is determined to take the value of $-12.92^\circ$, whichis in agreement with the value of $-13^\circ\sim-17^\circ$ deduced from arather exhaustive and up-to-date analysis of data. It is also pointed out thatthe omission of the flavor-dependent $q\bar{q}$ annihilation effect might be afactor resulting in the invalidity of Schwinger's original nonet mass formulafor pseudoscalar nonet.Comment: Latex, 7 page

Effects of Flavour-Dependent q q̄ Annihilation on the Mixing Angle of the Isoscalar Octet-Singlet and Schwinger's Nonet Mass Formula