  In this paper, we study the global stability of classical solutions to a
Keller--Segel equations in scaling-invariant spaces. We prove that for any
given $0<\mathcal{M}<1+\lambda_1$ with $\lambda_1$ being the first eigenvalue
of Neumann Laplacian, the initial--boundary value problem of the Keller--Segel
system has a unique globally bounded classical solution provided that the
initial datum is chosen sufficiently close to $(\mathcal{M},\mathcal{M})$ in
the norm of $L^{d/2}(\Omega)\times \dot{W}^{1,d}(\Omega)$ and satisfies a
natral average mass condition. Our proof is based on the perturbation theory of
semigroups and certain delicate exponential decay estimates for the linearized
semigroup. Our result suggests a new observation that nontrivial classical
solution for Keller--Segel equation can be obtained globally starting from
suitable initial data with arbitrarily large total mass provided that volume of
the bounded domain is large, correspondingly.
