A core intended to be used as a support for a roll of paper, especially toilet paper, is formed by winding at least one strip made of tissue, the strip being impregnated, at least locally, with starch so as to improve its stiffness. Thus configured, a core is provided having both a mechanical strength suitable for the envisaged use and a greatly improved ability to disintegrate relative to a cardboard core so as to allow it to be able to be disposed of directly in a toilet bowl without risk of blocking the soil pipe.