We report seven new eclipse timings for the novalike variable 1RXS J064434.5+334451. An analysis of our data, along with all previously available timings (36 published and 16 unpublished), yields a best-fitting linear ephemeris of BJD$_mathrm{ecl} = 2,453,403.7611(2) + 0.269~374~43(2)~mathrm{E}$. We find a somewhat improved fit with a quadratic ephemeris given by: BJD$_mathrm{ecl} = 2,453,403.7598 + 0.269~374~87~mathrm{E} - 2.0times10^{-11}~mathrm{E}^2$, which suggests that the orbital period may be decreasing at a rate given by $dot P simeq -1.5times10^{-10}$.
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