  We present the X- and $\gamma$-ray detection of GRB 990704 and the discovery
and study of its X-ray afterglow, 1SAX J1219.5-0350. Two pointed BeppoSAX
observations with the narrow field instruments were performed on this source,
separated in time by one week. The decay of the X-ray flux within the first
observation appears unusually slow, being best-fit by a power law with negative
index 0.83$\pm$0.16. Such a slow decay is consistent with the non-detection in
our second observation, but its back-extrapolation to the time of the GRB
largely underestimates the detected GRB X-ray prompt emission. In addition, the
GRB prompt event shows, among the BeppoSAX-WFC detected sample, unprecedentedly
high ratios of X- and gamma-ray peak fluxes (F$_{2-10 keV}$/F$_{40-700
keV}$$\sim$0.6, and F$_{2-26 keV}$/F$_{40-700 keV}$$\sim$1.6) and fluences
(S$_{2-10 keV}$/S$_{40-700 keV}$$\sim$1.5 and S$_{2-26 keV}$/S$_{40-700
keV}$$\sim$2.8), making it, among the BeppoSAX arcminute-localized GRBs, the
closest to the recently discovered class of Fast X-ray Transients.
