  We study the Dirac-Born-Infeld (DBI) action with one linear and one
non-linear supersymmetry in the presence of a constant Fayet-Iliopoulos (FI)
D-term added explicitly or through a deformation of supersymmetry
transformations. The linear supersymmetry appears to be spontaneously broken
since the D auxiliary field gets a non-vanishing vacuum expectation value and
an extra term proportional to the FI parameter involving fermions emerges in
the non-linear formulation of the action written recently. However in this
note, we show that on-shell this action is equivalent to a standard
supersymmetric DBI action ${\it without}$ FI term but with redefined tension,
at least up to order of mass-dimension 12 effective interactions.
