  Let n>0 be an integer and let B_{n} denote the hyperoctahedral group of rank
n. The group B_{n} acts on the polynomial ring
Q[x_{1},...,x_{n},y_{1},...,y_{n}] by signed permutations simultaneously on
both of the sets of variables x_{1},...,x_{n} and y_{1},...,y_{n}. The
invariant ring M^{B_{n}}:=Q[x_{1},...,x_{n},y_{1},...,y_{n}]^{B_{n}} is the
ring of diagonally signed-symmetric polynomials. In this article we provide an
explicit free basis of M^{B_{n}} as a module over the ring of symmetric
polynomials on both of the sets of variables x_{1}^{2},..., x^{2}_{n} and
y_{1}^{2},..., y^{2}_{n} using signed descent monomials.
