  We present preliminary results from a search for the flavor-changing neutral
current decays B-->Kl^+l^- and B-->K^*(892)l^+l^- using a sample of 22.7 x 10^6
Upsilon(4S)-->B anti-B decays collected with the BABAR detector at the PEP-II B
Factory. We have reconstructed the following final states: B^+ --> K^+l^+l^-,
B^0 --> K^0l^+l^- (K_s^0 --> pi^+pi^-), B^+ --> K^{*+}l^+l^- (K^{*+} --> K_s^0
pi^+), and B^0 --> K^{*0}l^+l^- (K^{*0} --> K^+pi^-), where l^+l^- is either an
e^+e^- or mu^+mu^- pair. We obtain the 90% C.L. upper limits BF(B --> Kl^+l^-)<
0.6 x 10^{-6} and BF(B --> K^*l^+l^-)<2.5 x 10^{-6}, close to the Standard
Model predictions for these branching fractions.
