NOVELTY - A polyarylene-type block copolymer contains a block (A) containing ion exchange group, and a block (B) which does not contain ion exchange group, and has ion exchange capacity of 3 m equivalent/g or more. The weight average molecular weight of block (A) and block (B) is 50000-1000000 and 8000-50000, respectively based on polystyrene conversion. The block (B) is obtained from a polymer which does not contain ion exchange group. The block (A) contains a structural unit (I). The block (B) contains structural unit (II).    USE - Polyarylene-type block copolymer is used for polymer electrolyte for polymer electrolyte membrane, polymer electrolyte composite film, catalyst composition, and membrane electrode assembly for polymer electrolyte-type fuel cell (all claimed).    ADVANTAGE - The polymer electrolyte membrane formed using polyarylene-type block copolymer has high proton-conductivity, high-temperature stability, and power generation characteristics.    DETAILED DESCRIPTION - A polyarylene-type block copolymer contains a block (A) containing ion exchange group, and a block (B) which does not contain ion exchange group, and has ion exchange capacity of 3 m equivalent/g or more. The weight average molecular weight of block (A) and block (B) is 50000-1000000 and 8000-50000, respectively based on polystyrene conversion. The block (B) is obtained from a polymer which does not contain ion exchange group. The block (A) contains a structural unit of formula: -(Ar1)- (I). The block (B) contains structural unit of formula: -(Ar2-X1)- (II).    Ar1=arylene optionally having substituents chosen from group A;    group A=1-20C alkyl, 1-20C alkoxy, 6-20C aryl, 6-20C aryloxy, 2-20C acyl, 1-20C alkylsulfonyl, cyano, 6-20C arylsulfonyl (all optionally substituted) or fluoro;    Ar2=aromatic group optionally having substituents chosen from group A;and    X1=-S- or -O-.    INDEPENDENT CLAIMS are included for the following:    (1) polymer electrolyte composite film, which comprises polymer electrolyte and porous base material; and    (2) catalyst composition, which comprises polymer electrolyte, and catalyst component.