This paper tries to determine how growth of money supply affects inflation in different time-horizons and under different inflation levels in the Czech Republic, Poland, Hungary and Russia. The research is done by using two innovative methodologies – the wavelet approach and Bayesian quantile regression. By observing these four countries, we can assess whether inflation targeting (IT) plays significant role in curbing inflation, because three Visegrad group countries adopted IT almost two decades ago, while Russia started to conduct IT relatively recently. Estimated quantiles suggest that money supply growth does not influence inflation in the Czech Republic and Hungary, whatsoever. We find that money growth impacts inflation in Poland, but very modestly. On the other hand, in the case of Russia, the transmission effect from money to inflation is much higher, and it goes around 40% in low inflation conditions, when M1 aggregate is observed, and around 78% in low inflation conditions, when M3 aggregate is analysed. The overall results clearly indicate that the adoption of the IT framework as a disinflation strategy proved to be successful in the Visegrad group countries, since excessive money growth has little or no effect at all on inflation in these countries.