The KTeV/E799 experiment at Fermilab has searched for the rare kaon decay K(L)-->pi(0)e(+)e(-). This mode is expected to have a significant CP violating component. The measurement of its branching ratio could support the standard model or could indicate the existence of new physics. This Letter reports new results from the 1999-2000 data set. One event is observed with an expected background at 0.99+/-0.35 events. We set a limit on the branching ratio of 3.5x10(-10) at the 90% confidence level. Combining with the previous result based on the data set taken in 1997 yields the final KTeV result: BR(K(L)-->pi(0)e(+)e(-))<2.8x10(-10) at 90% C.L.