The dimensionally regularized massless non-planar double box Feynman
diagram with powers of propagators equal to one, one leg off the mass shell,
i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is
analytically calculated for general values of q^2 and the Mandelstam
variables s,t and u (not necessarily restricted by the physical condition
s+t+u=q^2). An explicit result is expressed through (generalized)
polylogarithms, up to the fourth order, dependent on rational combinations of
q^2,s,t and u, and simple finite two- and three fold Mellin--Barnes
integrals of products of gamma functions which are easily numerically
evaluated for arbitrary non-zero values of the arguments.