The invention relates to a method for decellularising allogenic and xenogenic foreign material for the subsequent production of bioprostheses, coated with endogenous body cells, whereby the foreign material is firstly treated in a solution of bile acid and then alcohol, each with an intermediate or subsequent rinsing step, in combination with a mechanical action on the tissue and the cells by the force generated from a flowing treatment medium, at least in the final rinsing step. After said treatment the tissue is completely rid of foreign cell material and viruses and represents an excellent starting material for the coating with cells of the bioprosthesis recipient.