A method of manufacturing aromatic hydrocarbons, which are suitable for the production of terephthalic acid, from tall oil-based raw material. According to the invention, the raw material that contains tall oil or its fraction is catalytically deoxygenated with hydrogen, and one or more aromatic hydrocarbons that can be converted into terephthalic acid are separated from the deoxygenated reaction yield. The deoxygenation catalyst is a NiMo catalyst and, in addition, a cracking catalyst can be used, such as an acidic zeolite catalyst. The separated hydrocarbon can be p-xylene, o-xylene or p-cymene. According to the invention, these can be converted by oxidation and, when needed, by a re-arrangement reaction into terephthalic acid that is suitable for the source material of the manufacture of bio-based polyethylene terephthalate.