  We construct a zero-curvature Lax connection in a sub-sector of the
superstring theory on AdS(4) x CP(3) which is not described by the
OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet
fermions associated to eight broken supersymmetries of the type IIA background
are physical fields. As such, the prescription for the construction of the Lax
connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4)
does not do the job. So, to construct the Lax connection we have used an
alternative method which nevertheless relies on the isometry of the target
superspace and kappa-symmetry of the Green-Schwarz superstring.
