In the context of the new international relationships generated by the globalization phenomenon and of the effects of the economic and financial crisis, which has outburst in 2008, it became clear that the economic theories according to which monetary stability seems to be a necessary and sufficient condition for the existence of financial stability are no longer valid. But it can be accepted the idea that monetary stability is a contributor to the achievement of price stability, financial stability and macroeconomic stability, as well as to avoiding imbalances in the economy. In addition, the analysis of the causes of the crisis has shown that the direction of causal links between monetary and financial stability is in both ways: monetary stability affects financial stability and financial stability influences monetary stability. In these conditions, the high costs of the financial crises seem to indicate as necessary the involvement of central banks to a greater extent in the prevention of these crises, and implicitly in ensuring financial stability. In the article, the author argues the need for the central banks to involve in monitoring of the financial markets trends, as well as the opportunity of including financial stability among the objectives of central banks. Afterwards, there are reviewed the ways in which monetary stability can be improved, including the implementation of a strategy of monetary policy.