This paper presents a new method of reconstructing the individual charged and neutral hadrons in tau decays with the ATLAS detector. The reconstructed hadrons are used to classify the decay mode and to calculate the visible four-momentum of reconstructed tau candidates, significantly improving the resolution with respect to the calibration in the existing tau reconstruction. The performance of the reconstruction algorithm is optimised and evaluated using simulation and validated using samples of Z -> tau tau and Z(-> mu mu)+jets events selected from proton-proton collisions at a centre-of-mass energy root s = 8 TeV, corresponding to an integrated luminosity of 5 fb(-1).