The invention relates to a method for cooling a liquefied gas (8) stored in the inner space of a sealed, thermally insulating vessel (2) in a state of two-phase liquid-vapour equilibrium, said methodcomprising the steps of: drawing a stream of gas in vapour phase into the inner space of the vessel (2), said step of drawing a stream of gas in vapour phase generating in the inner space of the vessel a pressure P1 of less than the atmospheric pressure such that vaporisation of the liquefied gas is promoted and the liquefied gas stored in the vessel is placed in a state of two-phase liquid-vapourequilibrium, with the liquefied gas having a temperature of less than the liquid-vapour equilibrium temperature of said liquefied gas at atmospheric pressure; and guiding the drawn stream of gas in vapour phase towards a circuit for using gas in vapour phase (13). The invention also relates to a facility for storing and cooling a liquefied gas.