Letuq(s[(2)) denote the quantum enveloping algebra of s((2) over a field k. In this note we show that if q is a root of unity, then the coradical filtration {Hn}n≥0 ofuq(s[(2)) is the filtration by a certain degree function depending on the order ofq4and on the characteristic ofk. The degree function will be explicitly described in Section 2 for chars= 0 and in Section 3 for chark=s> 0.