We have detected neutral hydrogen absorption at 21 cm wavelength in the quasar-galaxy pair 3C 268.4/NGC 4138. The absorption spectrum exhibits two features which are separated by 65 and -120 km s/sup -1/, respectively, from the center velocity of 880 km s/sup -1/ of the neutral hydrogen emission profile from NGC 4138. The line of sight of the quasar 3C 268.4 is separated by approx.14 kpc (2'9) from NGC 4138 and lies very close (<5/sup 0/) to the minor axis of the galaxy where the radial component of its rotation velocity is small. This leads to the suggestion that in view of the large relative velocities of the neutral hydrogen clouds producing the observed features, they are situated in the halo region rather than in the disk of the galaxy. The detection of this second example of absorption in a close quasar-galaxy pair further weakens the argument for association of the quasar with the galaxy.