NOVELTY - Polymer has specific structural unit (I).    USE - For ion exchanger and proton conductor of fuel cell (all claimed) e.g. direct methanol fuel cell used for motor vehicles, domestic devices and portable apparatuses e.g. mobile telephone, mobile notebook personal computer, electronic still camera, personal digital assistant, video camera, handheld game machine, mobile server, mobile display, portable generator, field lighting equipment device, flash light, electronic drive bicycle, domestic robot and toys.    ADVANTAGE - The polymer has high ionic conductivity, and provides proton conductor with favorable methanol permeability. The fuel cell using the proton conductor has high output and favorable internal resistance.    DETAILED DESCRIPTION - Polymer has structural unit of formula (I).    A1=tetravalent atom group;    L1,L2=1-25C bivalent coupling group;    R1=alkyl, aryl or hetero cyclic group;    a=1-3;    b,c=1 or 0;    asterisk=position, which couples to silicon atom;and    asteriskasterisk=position, which couples to organic polymer chain.    INDEPENDENT CLAIMS are included for the following:    (i) ion exchanger containing the polymer;    (ii) proton conductor (11) containing the polymer;    (iii) fuel cell having the proton conductor; and    (iv) manufacture of proton conductor, which involves co-polymerizing organosilicon compound of formula (III) and silicon compound of formula (VI) and (VII) after oxidation, or vice versa.    A2=tetravalent group;    B2, B3=coupling group which contains aliphatic group and/or aromatic group;    R5, R7=alkyl or aryl group;    e, h, i=1-3;    q, r=1-4;    L3, L4=1-25C bivalent group;    R3=alkyl, aryl or hetero cyclic group;    R4, R6, R8=H atom, alkyl, aryl, silyl group;    f,g=0 or 1;and    Y=polymerizable group capable of forming carbon-carbon bond or carbon-oxygen bond by polymerization.    DESCRIPTION OF DRAWING(S) - The figure shows an outline sectional view of structure of catalyst electrode joining film using the proton conductor.    fuel cell electrode film composite (10)    proton conductor (11)    anode (12)    cathode (13)    cathode pole catalyst layer (13b)