Tetragonal　phase　(1-x)(0.875Bi(0.5)Na(0.5)TiO(3)-0.125BaTiO(3))-xBi(Mg0.5Ti0.5)O-3　lead-free　ferroelectrics　were　designed　and　fabricated　by　a　conventional　solid　state　route.　All　the　specimens　exhibit　a　tetragonal　perovskite　structure,　and　undergo　a　phase　evolution　from　ferroelectric　P4mm　to　antiferroelectric　relaxor　P4bm　as　the　BMT　addition　increases.　The　critical　composition　x　=　0.04　makes　a　bridge　between　the　both　tetragonal　phases,　and　gives　a　large　field-induced　strain　of　0.30%　and　an　adequately-large　electrostrictive　coefficient　Q(33)　of　0.0254　m(4)/C-2.　To　be　highlighted,　the　field-induce　strain　of　the　composition　x　=　0.04　shows　an　almost　constant　value　over　the　temperature　range　of　18-100　degrees　C,　illustrating　a　temperature-insensitive　behavior,　which　could　be　attributed　to　the　widened　gap　between　TR-E　and　TF-R.　The　temperature-insensitive　large　strain　of　the　tetragonal　BNT-BT-BMT　composition　give　a　promising　potential　for　application　in　precision　position　actuators.