Fig. 7 compares the fit using the simple log-periodic formula shown as the continuous red line (which is the same as the continuous black line in Fig. 3) with the fit using the log-periodic formula derived from a second-order Landau expansion shown as the red dashed line. In our paper appeared in the December issue of Quantitative Finance in 2002, we stated that the simple log-periodic formula is enough to fit the S&P 500 antibubble and we thus concluded that the S&P 500 index had not yet entered into the second phase in which the angular log-frequency may start its shift to another value, as did the 1990 Nikkei antibubble after about 2.5 years. This figure confirms our announcement in our update of September 17, 2003 that we now detect the occurrence of such a change of regime. The statistical tests summarized at the end of our update of September 17, 2003 and given in details in "Testing the Stability of the 2000-2003 US Stock Market Antibubble" give the probability (shown as the full black dots and the right vertical scale) to reject the hypothesis that the market has entered the second phase in which the angular log-frequency is shifting to another value. These results here open very seriously the possibility that, indeed, we have entered a cross-over regime in log-frequency shift. The improved second-order log-periodic formula shown as the red dashed line suggests that there will be a delay in the expected drop, which rather than occurring now, may wait until November-December 2003. Another possibility discussed in our recent paper "Testing the Stability of the 2000-2003 US Stock Market Antibubble" is that the antibubble may have ended and the market is in a new regime. Our analysis does not select this scenario as the prefered one.