Process for the preparation of an aqueous albumin solution from an albumin starting solution, which contains stabilizing molecules that can occupy albumin binding sites, wherein during the procedure for increasing the albumin binding capacity for Other molecules are removed from the albumin of the albumin starting solution at least a part of the stabilizing molecules and separated from the albumin starting solution, a) by contacting the albumin starting solution with a solid adsorbent material, whose affinity for at least one part, preferably for all the stabilizing molecules used, is higher than the affinity of the albumin for the corresponding stabilizing molecules, in which the adsorbent material is a particulate activated carbon material, which is packaged in a column or a bed or is embedded in a support matrix, so that between the parts adsorbent material cells are formed permeable channels to liquids, the average diameter of the channels being, with respect to the entire length of the channels configured between the particles of all the adsorbent material used, greater than 100 nm and less than 1000 μm and the The procedure is carried out at a pH value>; = 5 and b) separating the albumin solution from the adsorbent material.Procedimiento para la preparación de una solución acuosa de albúmina a partir de una solución de partida de albúmina, que contiene moléculas estabilizadoras que pueden ocupar sitios de unión de la albúmina, en donde durante el procedimiento para el aumento de la capacidad de unión a albúmina para otras moléculas se elimina de la albúmina de la solución de partida de albúmina al menos una parte de las moléculas estabilizadoras y se separa de la solución de partida de albúmina, a) poniéndose en contacto la solución de partida de albúmina con un material adsorbente sólido, cuya afinidad por al menos una parte, preferentemente para todas las moléculas estabilizadoras usadas, es más alta que la afinidad de la albúmina por las correspondientes