Based on the quantum defect theory, the infinite Rydberg states and its adjacent continue states with the same angular moment property will form a channel. Previous studies have considered the collision-induced transitions from a single initial state to a final channel. Here we extend these thoery to include all possible transitions between two channels. By defining a renormalized generalized oscillator strength density (GOSD) which varies smoothly across threshold, the inelastic collisions from an initial channel to a final channel can be treated in a unified manner. As an example, we present the renormalized GOSD of the Rb atom from s-initial to p-final channel, and also from s-initial to s-final channel.