A method for replenishing the supply of cryogenic liquid from a storage tank (2) includes: pressurizing a container (14) with cryogenic gas at a first pressure, said container having passing through it a first cryogenic fluid flow line referred to as the cold line and a second cryogenic fluid flow line referred to as the hot line, passing cryogenic liquid at a second pressure through the cold line (12), and supplying the container (14) with cryogenic gas at least partially from cryogenic liquid pumped from the storage tank (2) and vaporized. A device is also provided for the method hereinabove.