This invention relates to a process in which a linear olefin is converted under isomerizing conditions to its corresponding methyl branched isoolefin by contact at a temperature of from 200.degree. C. to 650.degree. C. with an isomerizing catalyst comprising (i) at least one zeolite having only in one dimension a pore structure having a pore size small enough to retard by-product dimerization and coke formation and large enough to permit entry of the linear olefin and allow formation of the methyl branched isoolefin, (ii) an alumina binder and (iii) up to about 15% by weight of coke oxidation-promoting metal. After a period of operation, when sufficient coke has deposited on the catalyst in an amount to significantly reduce the activity of the catalyst, the catalyst is stripped of hydrocarbon and then contacted at elevated temperature with an oxygen-containing gas for a sufficient time to burn off the coke, i.e., to regenerate the catalyst at a temperature of less than about 565.degree. C. After regeneration, the isomerization process is continued. The use of palladium and/or platinum as the coke oxidation-promoting metal is particularly desirable.