Improved Kennedy-Thorndike experiment to test special relativity.

We have carried out a modern version of the Kennedy-Thorndike experiment by searching for sidereal variations between the frequency of a laser locked to an ${\mathit{l}}_{2}$ reference line and a laser locked to the resonance frequency of a highly stable cavity. No variations were found at the level of 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$. This represents a 300-fold improvement over the original Kennedy-Thorndike experiment and allows the Lorentz transformations to be deduced entirely from experiment at an accuracy level of 70 ppm.