A method for balancing a battery comprising a plurality of branches (Ba, Bb,..., Bn) in parallel, each branch comprising at least two electrochemical cells in series (E1a, E2a, E3a, E1b, E2b, E3b), an activatable electrical energy discharge or transfer device (Rb) connected across the terminals of each electrochemical cell, said method comprising the following successive steps: a) measuring a voltage across each electrochemical cell (V1a, V2a, V3a, V1b, V2b, V3b) in a configuration where all the electrical energy discharge or transfer devices are not activated; b) determining a lowest voltage and a highest voltage out of all the voltages measured in step a); c) calculating a difference ΔV between the lowest voltage and the highest voltage from step b); d) if ΔV exceeds a predetermined threshold value ΔVs1: - activating the electrical energy discharge or transfer device(s) connected across the terminals of the cell(s) of that branch which includes the electrochemical cell having the lowest voltage with the exception of the electrical energy discharge or transfer device associated with the electrochemical cell having the lowest voltage, simultaneously with: - deactivating the electrical energy discharge or transfer devices connected across the terminals of the cells of the branch or branches that do not include the electrochemical cell with the lowest voltage; e) measuring a voltage across each electrochemical cell; f) determining a lowest voltage and a highest voltage out of all the voltages measured in step e); g) calculating a difference ΔV between the lowest voltage and the highest voltage; h) if ΔV is less than a predetermined threshold value ΔVs2, strictly below ΔVs1, deactivating all discharge devices. a) measuring a voltage across each electrochemical cell (V1a, V2a, V3a, V1b, V2b, V3b) in a configuration where all the electrical energy discharge or transfer devices are not activated; b) determining a lowest voltage and a highest voltage out of all the voltages measured in step a); c) calculating a difference ΔV between the lowest voltage and the highest voltage from step b); d) if ΔV exceeds a predetermined threshold value ΔVs1: - activating the electrical energy discharge or transfer device(s) connected across the terminals of the cell(s) of that branch which includes the electrochemical cell having the lowest voltage with the exception of the electrical energy discharge or transfer device associated with the electrochemical cell having the lowest voltage, simultaneously with: - deactivating the electrical energy discharge or transfer devices connected across the terminals of the cells of the branch or branches that do not include the electrochemical cell with the lowest voltage; - activating the electrical energy discharge or transfer device(s) connected across the terminals of the cell(s) of that branch which includes the electrochemical cell having the lowest voltage with the exception of the electrical energy discharge or transfer device associated with the electrochemical cell having the lowest voltage, simultaneously with: - deactivating the electrical energy discharge or transfer devices connected across the terminals of the cells of the branch or branches that do not include the electrochemical cell with the lowest voltage; e) measuring a voltage across each electrochemical cell; f) determining a lowest voltage and a highest voltage out of all the voltages measured in step e); g) calculating a difference ΔV between the lowest voltage and the highest voltage; h) if ΔV is less than a predetermined threshold value ΔVs2, strictly below ΔVs1, deactivating all discharge devices.