We study T-violating triple-product asymmetries in the quark-level decay b
--> s u (u) over bar within the standard model (SM). We find that only two
types of triple products axe non-negligible. First, the asymmetry in (p) ov
er right arrow (u).((s) over right arrow (u) x (s) over right arrow ((u) ov
er bar)) or (p) over right arrow ((u) over bar).((s) over right arrow (u) x
(s) over right arrow ((u) over bar)) can be as large as about 5%. It can b
e probed in B-->V1V2 decays, where V-1 and V-2 are vector mesons. Second, t
he asymmetry in (s) over right arrow (b).((p) over right arrow (u) x (p) ov
er right arrow (s)) can be in the range 1-3%. One can search for this signa
l in decays such as Delta (b)-->Lambda pi (+)pi (-). All other triple-produ
ct asymmetries are expected to be small within the SM. This gives us new me
thods of searching for new physics.