  We organize the eight variables of the four-dimensional bosonic string ({\dot
X}^{\mu}, X'^{\mu}) into a 2 x 2 x 2 hypermatrix a_{AA'A''} and show that in
signature (2,2) the Nambu-Goto Lagrangian is given by \sqrt{Det a} where Det is
Cayley's hyperdeterminant. This is invariant not only under [SL(2,R)]^{3} but
also under interchange of the indices A, A' and A''. This triality reveals
hitherto hidden discrete symmetries of the Nambu-Goto action.
