Аннотация:t is well-known that de Sitter Lie algebra o(1,4) contrary to anti-de Sitter one o(2,3) does not have a standard ℤ2-graded superextension. We show here that the Lie algebra o(1,4) has a superextension based on the ℤ2×ℤ2-grading. Using the standard contraction procedure for this superextension we obtain an {\it alternative} super-Poincar\'e algebra with the ℤ2×ℤ2-grading.