Electron temperature gradient driven instability in toroidal plasmas with negative magnetic shear is studied.Full electron kinetics is considered, and the behaviours of the modes and corresponding turbulent transport in the parameter regimes close to the instability threshold are emphasized. Growing and damped modes are both investigated.The singular points of the integrand are disposed of, and the fitting formulae for the critical gradient are given. The theoretical results are shown to be close to the experimental observations.