  The explicit expressions for the strong and the weak rigorous multiplicative
perturbation bounds for the Generalized block Cholesky downdating problem are
obtained. By bringing together the modified matrix-vector equation approach
with the method of Lyapunov majorant function and the Banach fixed point
theorem, we derived the strong rigorous multiplicative perturbation bounds. By
using the matrix-equation approach the weak rigorous multiplicative bounds are
presented. Numerical experiments are provided to illustrate the obtained
results.
