The　existence　and　propagation　of　transverse　surface　waves　in　piezoelectric　coupled　solids　is　investigated,　in　which　perfect　bonding　between　a　metal/dielectric　substrate　and　a　piezoelectric　layer　of　finite-thickness　is　assumed.　Dispersion　equations　relating　phase　velocity　to　material　constants　for　the　existence　of　various　modes　are　obtained　in　a　simple　mathematical　form　for　a　piezoelectric　material　of　class　6　mm.　It　is　discovered　and　proved　by　numerical　examples　in　this　paper　that　a　novel　Bleustein-Gulyaev　(B-G)　type　of　transverse　surface　wave　can　exist　in　such　piezoelectric　coupled　solid　media　when　the　bulk-shear-wave　velocity　in　the　substrate　is　less　than　that　in　the　piezoelectric　layer　but　greater　than　the　corresponding　B-G　wave　velocity　in　the　same　piezoelectric　material　with　an　electroded　surface.　Such　a　wave　does　not　exist　in　such　layered　structures　in　the　absence　of　piezoelectricity.　The　mode　shapes　for　displacement　and　electric　potential　in　the　piezoelectric　layer　are　obtained　and　discussed　theoretically.　The　study　extends　the　regime　of　transverse　surface　waves　and　may　lead　to　potential　applications　to　surface　acoustic　wave　devices.