  We study the quantum phase transition from an antiferromagnetic metal to a
heavy fermion metal in the Kondo lattice model. Based on the strong coupling
approach we {\it first} diagonalize the Kondo coupling term. Since this strong
coupling approach makes the resulting Kondo term {\it relevant}, the Kondo
hybridization persists even in the antiferromagnetic metal, indicating that
fluctuations of Kondo singlets are not critical in the phase transition. We
find that the quantum transition in our strong coupling approach results from
{\it softening of antiferromagnetic spin fluctuations of localized spins},
driven by the Kondo interaction. Thus, the volume change of Fermi surface
becomes continuous across the transition. ......
