To obtain the subject composition improved in cosmetic characteristics such as easiness of unraveling, smoothness and pliability of hair by including a specific conditioner and a specified amphoteric polymer in a medium.

This composition comprises (A) at least one conditioner selected from a synthetic oil, a vegetable oil, a vegetable wax and a ceramide type compound and (B) at least one amphoteric polymer containing at least one kind of monomer of an acrylate or a methacrylate or an acrylamide or a methacrylamide type having at least one 8-30C aliphatic chain. The above amphoteric polymer preferably contains the aliphatic chain-containing monomer in an amount of 1-20 mol%, preferably 1.5-15 mol% based on the total number of mol of the monomer. For example, a monomer represented by the formula (R1 and R2 are each H or methyl; R3 to R5 are each a 1-30C alkyl; Z is NH or O; (n) is 2-5; A- is an anion derived from an organic or an inorganic acid) is cited as the monomer used.