Abstract: A dialysis membrane for hemodialysis with improved biocompatibility is composed of a modified cellulose which has a structure represented by the formula ##STR1## Cell is the framework of the unmodified cellulose molecule or of the chitin molecule, in each case without hydroxyl groups. Z is an atom of group V or VI (except oxygen) of the periodic system. Where Z is an atom of group V, T is a hydrogen atom or (X-Y). Where Z is an atom of group VI, T is omitted. (n+s) indicates the mean degree of substitution with 0<n<m and 0.ltoreq.s<m and n+s<m. m=3 in the case of the unmodified cellulose molecule and m=2 in the case of the chitin molecule. -X- can be omitted as desired or -X- and -X'- denote specific divalent groups. -Y and -Y' denote -H and/or specified univalent radicals. X is identical to or different from X' and Y is identical to or different from Y'.