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.
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