A deep exposure of the bright star Arcturus (alpha-Bootis: K1 III) with the Rontgensatellit (ROSAT) failed to detect soft X-ray emission from the archetype "noncoronal" red giant. The 3-sigma upper limit in the energy band 0.1-2.4 keV corresponds to an X-ray luminosity of less than 3 x 10(25) ergs s-1, equivalent to a coronal surface flux density of less than 1 x 10(-4) solar. The nondetection safely eliminates coronal irradiation as a possible mechanism to produce the highly variable He I lambda-10830 feature and emphasizes the sharp decline in solar-like coronal activity that accompanies the evolution of low-mass single stars away from the main sequence. While the most conspicuous object in the ROSAT field of view was not visible in X-rays, at least one fainter star is among the almost-equal-to 60 sources recorded: the delta-Sct variable CN Boo, an A8 giant in the UMa Stream.