  We formulate a new criterion for regularity of a suitable weak solution v to
the Navier-Stokes equations at the space-time point (x_0,t_0). The criterion
imposes a Serrin-type integrability condition on v only in a backward
neighbourhood of (x_0,t_0), intersected with the exterior of a certain
space-time paraboloid with vertex at point (x_0,t_0). We make no special
assumptions on the solution in the interior of the paraboloid.
