  Multifractal analysis and extensive statistical tests are performed upon
intraday minutely data within individual trading days for four stock market
indexes (including HSI, SZSC, S&P500, and NASDAQ) to check whether the indexes
(instead of the returns) possess multifractality. We find that the mass
exponent $\tau(q)$ is linear and the singularity $\alpha(q)$ is close to 1 for
all trading days and all indexes. Furthermore, we find strong evidence showing
that the scaling behaviors of the original data sets cannot be distinguished
from those of the shuffled time series. Hence, the so-called multifractality in
the intraday stock market indexes is merely an illusion.
