  Let B_n be the hyperoctahedral group; that is, the set of all signed
permutations on n letters, and let B_n(T) be the set of all signed permutations
in B_n which avoids a set T of signed patterns. In this paper, we find all the
cardinalities of the sets B_n(T) where $T \subseteq B_2$. This allow us to
express these cardinalities via inverse of binomial coefficients, binomial
coefficients, Catalan numbers, and Fibonacci numbers.
