A process for obtaining a tertiary olefin, e.g. isobutylene in a very pure state by decomposing the corresponding ether, e.g. methyl tert. butyl ether, in the presence of a catalyst constituted by silica, modified by the addition of at least one element or compound of an element preferably chosen from the group constituted by rubidium, cesium, magnesium, calcium, strontium, barium, gallium, lanthanum, cerium, praseodymium, neodymium and uranium and optionally by the addition of at least one element or compound of an element chosen from the group constituted by aluminium, titanium and zirconium.