  We identify a finite wavenumber instability of a 90$^{\circ}$ tilt grain
boundary in three dimensional lamellar phases which is absent in two
dimensional configurations. Both a stability analysis of the slowly varying
amplitude or envelope equation for the boundary, and a direct numerical
solution of an order parameter model equation are presented. The instability
mode involves two dimensional perturbations of the planar base boundary, and is
suppressed for purely one dimensional perturbations. We find that both the most
unstable wavenumbers and their growth rate increase with $\epsilon$, the
dimensionless distance away from threshold of the lamellar phase.
