I have discovered spectroscopic variations correlated with the photometric near-infrared (NIR) light curve in η Carinae. The fading of the high-excitation lines is coincident with the peaks in the NIR light curve, strongly resembling an S Doradus type of variability. The cycle, however, is highly stable, and the 5.52 yr period fits well all the shell episodes reported in the last 50 years. This period also recovers the three historical bursts of the last century, in phase with the present low-amplitude oscillations, which suggests a connection between the S Doradus cycle and the giant bursts. The present data reveal that η Car is continuously varying in the He I λ10830 line by thousands of solar luminosities. The last spectra in this line show that the low-excitation phase is already in progress. A test for the strict periodicity will be the confirmation of the central phase epoch of the next shell event, predicted to occur in 1997 December. A very sensitive mapping technique is also proposed for this occasion, in order to prove Homunculus geometry.