Fig. 7 compares the fits of S&P 500 from Aug. 9, 2000 to Dec. 16, 2003 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 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. However, we have found in our paper "Testing the Stability of the 2000-2003 US Stock Market Antibubble" that the market might have started to cross-over from the first-order to the second-order formula. This figure 7 further confirms our announcement that we now detect the occurrence of such a change of regime in log-frequency shift.