  We report on the isotope shift between ${}^{88}$Sr and ${}^{87}$Sr on the
${}^1S_0 - {}^3P_0$ clock transitions. The interleaved operation of an optical
lattice clock with two isotopes allows the canceling out of common
perturbations, such as the quadratic Zeeman shift, the clock-light shift, and
the blackbody radiation shift. The isotope shift is determined to be 62 188
134.004(10) Hz, where the major uncertainty is introduced by the collisional
shift that is distinct for each isotope. Our result allows us to determine the
frequency of $^{88}$Sr-$^{87}$Sr optical lattice clocks with a fractional
uncertainty of $2\times 10^{-17}$. The scheme is generally applicable for
measuring the isotope shift with significantly reduced uncertainty.
