The cathode sheath in a cold‐cathode Penning discharge operating in the high‐pressure mode has been investigated by using an rf impedance method. The effect of the presheath lying between the sheath and the plasma has been taken into consideration in deriving the sheath parameters from the impedance of the discharge, measured at two frequencies, under various discharge conditions. The sheath thickness and the dc incremental resistance of the sheath are found to decrease with the discharge current (the static magnetic field being held fixed), while these parameters decrease first, and then remain almost unchanged, if the magnetic field is increased (the discharge current being kept constant).