Black p-brane solutions for a wide class of intersection rules and Ricci-flat "internal" spaces are considered. They are defined up to moduli functions Hs obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra A3 is obtained. The functions H1, H2 and H3 for this solution are polynomials of degree 3, 4 and 3, correspondingly. An example of A3-solution with three 3-branes in 12-dimensional model (suggested by N. Khviengia et al.) is presented. © 2002 Elsevier Science B.V. All rights reserved.