The incommensurately modulated structure of tantalum tetratelluride (TaTe4) has been determined by X-ray diffraction on the basis of a 2a x2a x3c supercell. Mo Ka radiation, A=0.71069/~, /z= 405.0 cm -~. The space group of the subcell is P4/mcc, that of the supercell P4/ncc. a=6.5154(5), c= 6-8118 ~, RF =0.064 for 6422 observed reflections.The structure is characterized by TaTe4 chains along the c axis. These chains are modulated in such a way that Ta3 clusters are formed. The Te atoms respond to the displacements of the Ta atoms, keeping the bonds of the Te dimers, which link the chains, equal in length. The clusters in neighbouring chains are shifted with respect to each other with a phase shift of ~, causing the doubling of the a axis. A simple model is proposed to account for the observed modulations in NbTe4 and TaTe4.