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.
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