The authors present the results of a new measurement of the t{anti t} production cross section using e{mu} channel in p{anti p} collisions at {radical}s = 1.8 TeV. This study corresponds to an integrated luminosity of 108.3 {+-} 5.7 pb{sup {minus}1} acquired by the D0 detector during the Fermilab Tevatron Collider Run 1 (1992--1996). By using neural network techniques instead of the conventional analysis methods, the authors show that the signal acceptance can be increased by 10% (for m{sub t} = 172 GeV/c{sup 2}) while the background remains constant. Four e{mu} events are observed in data with an estimated background of 0.22 {+-} 0.14 corresponding to a t{anti t} production cross section of 9.75 {+-} 5.53 pb.