We acquired spectra for a random sample of galaxies within a 0.83 square degree region centered on the core of the Centaurus cluster .
Radial velocities were obtained for 225 galaxies to limiting magnitudes of V < 19.5 .
Of the galaxies for which velocities were obtained , we find 35 % to be member galaxies .
New redshifts are obtained for 15 Centaurus cluster members , many of these dwarf galaxies .
Radial velocities for the other members agree well with those from previous studies .
Of the 78 member galaxies , magnitudes range from 11.8 < V < 18.5 ( -21.6 < M _ { V } < -14.9 for H _ { \circ } = 70 km s ^ { -1 } Mpc ^ { -1 } ) with a limiting central surface brightness of \mu _ { \circ } < 22.5 mag arcsec ^ { -2 } .
While many of these galaxies are giants , about 25 galaxies with M _ { V } > -17.0 are considered dwarfs .
We constructed the cluster galaxy luminosity function by using these spectroscopic results to calculate the expected fraction of cluster members in each magnitude bin .
The faint-end slope of the luminosity function using this method is shallower than the one obtained using a statistical method to correct for background galaxy contamination .
We also use the spectroscopy results to define surface brightness criteria to establish membership for the full sample .
Using these criteria , we find a luminosity function very similar to the one constructed with the statistical background correction .
For both , we find a faint-end slope \alpha \sim - 1.4 .
The error in faint-end slope for the statistically corrected LF is \sim \pm 0.2 .
Adjusting the surface brightness membership criteria we find that the data are consistent with a faint-end slope as shallow as -1.22 or as steep as -1.50 .
We describe in this paper some of the limitations of using these methods for constructing the galaxy luminosity function .
This is paper II in our investigation of the cluster galaxy luminosity function .