We search for the decay B0-->rho(0)rho(0) in a data sample of about 227x10(6) Upsilon(4S)-->BB decays collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider at SLAC. We find no significant signal and set an upper limit of 1.1x10(-6) at 90% C.L. on the branching fraction. As a result, the uncertainty due to penguin contributions on the Cabibbo-Kobayashi-Maskawa unitarity angle alpha measured in B-->rhorho decays is decreased to 11 degrees at 68% C.L.