The long-term stratospheric carbon tetrafluoride (CF4) increase has been determined from infrared high spectral resolution solar occultation Fourier transform spectrometer measurements between 3 and 50 hPa (~20 to 40 km altitude) and latitudes from 50¿N to 50¿S during 1985, 1992, 1993, 1994, and 2004. The 1985 to 1994 measurements were recorded from the ATMOS (Atmospheric Trace MOlecule Spectroscopy) instrument at 0.01 cm-1 resolution and in 2004 by the Atmospheric Chemistry Experiment (ACE) instrument at 0.02 cm-1 resolution. Stratospheric volume mixing ratios, inferred from a polynomial fit to averages from the time periods considered here, increased from 49.37 ¿ 2.60 pptv (10-12 per unit volume) in 1985 to 58.38 ¿ 4.14 pptv in 1992, 60.46 ¿ 2.97 pptv in 1993, 60.11 ¿ 3.60 pptv in 1994 and to 70.45 ¿ 3.40 pptv in 2004. The stratospheric CF4 mixing ratio has continued to increase but at a slower rate than in previous years, for example, (1.14 ¿ 0.68)% yr-1 in 2004 as compared to (2.77 ¿ 0.47)% yr-1 in 1985, 1 sigma. Correlations of CF4 with N2O taking into account the increase of N2O with time also show the increase in the stratospheric CF4 burden over the two decade measurement time span. Our space-based measurements show that the slowdown in the rate of CF4 accumulation previously reported from surface measurements through 1997 has propagated to the stratosphere and is continuing.