NOVELTY - The method involves determining lowest and highest gear ratio set-points of a transmission based on lowest and highest non-electric engine rotational speed limitations. The lowest gear ratio set-point is modified to slow a non-electric engine i.e. internal combustion (IC) engine, below the lowest non-electric engine rotational speed limitation when a hybrid vehicle is in a coasting mode. Termination of the coasting mode of the vehicle is determined. The lowest gear ratio set-point is restored. The non-electric engine is accelerated to the lowest non-electric engine rotational speed limitation.    USE - Method for operating a transmission of a recuperation device i.e. regenerative braking system, integrated hybrid vehicle.    ADVANTAGE - The lowest set point is modified to slow the non-electric engine below the lowest non-electric engine rotational speed limitation when the vehicle is in the coasting mode, thus reducing the engine drag and maximizing recuperation energy. The rotational speed of the non-electric engine in the vehicle is reduced while the engine is in a coasting condition, and the power taken up by the engine during coasting is reduced, thus leaving a larger amount of power available to be recuperated by the recuperation device. The method enables the vehicle to operate efficiently and with less fuel consumption by reducing the need of the vehicle to generate power. The mass flow rate of the exhaust gases is lowered by reducing the engine rotational speed, thus slowing down the cooling of components of the exhaust system that is required to be remained at a specified temperature to operate optimally, and avoiding the need to turn ON the engine for maintaining the exhaust system temperature.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method for recuperating kinetic energy of a vehicle transmission.    DESCRIPTION OF DRAWING(S) - The drawing shows a block diagram illustrating a process of controlling shifting of hybrid vehicle transmission during and after the coasting mode of the vehicle.