The invention relates to a method for producing mainly ethylenically unsaturated isobutene polymers, wherein the sum of proportions of molecules with a double bond in an α position and molecules with a double bond in a position β is increased to 75% mol by polymerising isobutene in a liquid phase in the presence of a diluted or dispersed catalyst complex which comprises (i) an electron donor and (ii) a compound of general formula (I) HaMeb[MFx]c, wherein Me is a metal with oxidation state m, M is an element selected from elements of the groups 2, 3, 4, 5, 10, 11, 13, 14 or 15 of the periodic table according to the IUPAC notation of an element oxidation number n, a is an integer ≧1, b is an integer ≧0, x is an integer ≧2 and c is [(a+mb)/(x−n)]. The catalyst is preferably embodied in the form of HBF4O(CH3)2. The inventive method makes it possible to obtain an isobutene polymer having a low fluorine-content even using technical C4 hydrocarbon portions as an isobutene source.