A new necessary condition for the validity of the Riemann hypothesis

It is obtained results related to the Riemann function $\xi(s)$ which give a new necessary condition for the validity of Riemann hypothesis on the zeros of the classical zeta-function. It is proved that if at least one even derivative of the function $\xi(s)$ at the point $s = 1/2$ is not positive, then the Riemann hypothesis would be false. However, it is also proved that all the even derivatives at the point $s = 1/2$ are strictly positive and their asymptotic form for the order of derivatives tending to ininity is found.