To obtain enhanced toxicity to cancer cells from a chemotherapy medicine, and to control harmful effects of chemotherapy medicine on normal cells, by administering a specific compound, and then administering the chemotherapy medicine to cancer cells.

First, (A) a compound, which controls proliferation of normal cells, promotes proliferation of malignant cells and is not a compound of the formula I (X and Y are each chlorine or bromine; (o) and (p) are each 0 or 1; R1 and R2 are each a 1-3C alkyl or bonded to form a nitrogen atom- containing heterocyclic ring; (n) is 1-3) in an amount sufficient to inhibit an intercellular histamine bond in normal cells is administered to an animal and then (B) a chemotherapy medicine for cancer cells is administered to the animal. A compound of formula II (R1, R1 and (n) are as shown in the formula I) is preferable as the component A. The compound of formula II is a new compound and for example, N,N-diethyl-2-[4-(4'-fluorophenone)phenoxy]ethanolamine may be cited as the compound.