A method for tanning animal skin may include: putting the animal skin in contact with a first tanning bath comprising (weight percentages referring to a pelt weight of the animal skin): water, at least one C2-C8 aliphatic dialdehyde in a quantity within a range of 2%-30%, and/or at least one non-ionic surfactant in a quantity within a range of 0.1%-20%, wherein the first tanning bath has a pH within a range of 1-5 and a density within a range of 3° Bé-10° Bé; bringing the pH of the first tanning bath to a pH greater than 5 and less than or equal to 8; and/or washing the animal skin to obtain a tanned animal skin.