Method for dimerization of ethylene comprising a step for treatment of the reaction effluent

Method for treatment of the raw effluent that is obtained directly from a step for dimerization of ethylene into but-1-ene that comprises bringing into contact a catalytic composition that comprises at least one titanium compound of general formula [Ti(OR2)4] and at least one preformed mixture between a Lewis-base (BL)-type additive and an aluminum (Al) compound of general formula Al(R3)mY3-m and an ethylene feedstock, in which the treatment of the effluent comprises a step for neutralization of said raw effluent by adding at least one alcohol of general formula R1OH, in pure form or in solution in a solvent, in which R1 is an alkyl group, linear or branched, which contains from 6 to 20 carbon atoms, an aryl or aralkyl group that contains from 5 to 30 carbon atoms.