IUE spectra of Mg II h and k in late type dwarfs and giants were used to detect and measure absorption components due to the LISM. This technique gives a method of probing the awkward range from d = 3 pc to d = 80 pc from the Sun. In spite of interpretational uncertainties the HI component of the LISM can be plotted well enough to confirm it as a cloud some 20 to 30 pc in extent, peaking sharply in density towards l(II)-25 deg., moving towards the Sun from l(II)-25 deg, b(II) = + 10 deg., at 28 Km/sec. The hole towards l(II) = 150 deg is confirmed, suggesting a solar position close to the cloud's edge in this direction.