Exactly solvable p-brane model with extra supersymmetry

Effect of the supersymmetry enhancement due to the presence of tensor central charge coordinates in the models of tensionless superstring and superbrane is studied. Exactly solvable super p-brane model preserving 3/4 of the D=4, N=1 supersymmetry is presented. The fine tuning of extra κ-symmetry with the R-symmetry is observed. We show that the general solution for the Goldstone fermion is pure static.