We report on the analysis from ~110 ks of X-ray observations of Centaurus A carried out with the Proportional Counter Array (PCA) and the High Energy X-ray Timing Experiment (HEXTE) instruments on Rossi X-ray Timing Explorer (RXTE) during three monitoring campaigns over the last 4 years (10 ks in 1996, 74 ks in 1998, and 25 ks in 2000). The joint PCA/HEXTE X-ray spectrum can be well described by a heavily absorbed power law with photon index 1.8 and a narrow iron line due to fluorescence of cold matter. The measured column depth decreased by about 30% between 1996 and 2000, while the detected 2-10 keV continuum flux remained constant between 1996 and 1998, but increased by 60% in 2000. Since in all three observations the iron line flux did not vary, a corresponding decrease in equivalent width was noted. No appreciable evidence for a reflection continuum in the spectrum was detected. We present the interpretation of the iron line strength through Monte Carlo computations of various geometries. No significant temporal variability was found in Cen A at time scales from days to tens of minutes.