An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in 7Li+ ions at v=0.064c have been measured in the forward and backward direction to an accuracy of Deltanu/nu=1 x 10(-9) using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of 2.2 x 10(-7) for deviations from the time dilation factor gamma(SR)=(1-v2/c2)(-1/2).