The invention relates to an albumin-purification method comprising a step consisting in subjecting an aqueous albumin solution, with a concentration of between 15 g/l and 80 g/l and a pH of not lass than 7, to nanofiltration in a temperature range of between 15 DEG C and 55 DEG C. The invention also relates to: a virally-safe aqueous albumin solution which can be obtained using the inventive method and in which the sites for the transport and binding of the active therapeutic ingredients of the albumin are available; and an albumin composition for therapeutic use, which is obtained by adapting the albumin solution that is intended for clinical use.