We present a detailed description of the method and results of our cal
culation of the kaon B parameter using the Wilson quark action in quen
ched QCD at beta = 5.9-6.5. The mixing problem of the Delta s = 2 four
-quark operators is solved non-perturbatively with full use of chiral
Ward identities. We find B-K(NDR, 2GeV) = 0.562(64) in the continuum l
imit, which agrees with the value obtained with the Kogut-Susskind qua
rk action.