This paper re‐examines the relationship between inflation and economic growth in developing countries. Both the theoretical and the empirical literature are extremely divided on this issue. We apply a relatively new empirical technique – the continuous wavelet transform – to Bangladesh. Bangladesh is of interest because of its remarkable economic growth and poverty reduction during the last 30 years in combination with, for a developing country, a controlled inflation. The wavelet analysis is a contribution because it displays how the correlation and the lead–lag structure between variables change over timescales, taking into account that growth and inflation can follow several different cycles. Comovements between variables are generally studied in the time domain. Results from studies in the time‐domain study can be sensitive to the frequency of observations. On the other hand, studies in the frequency domain are not easily translated into time domains that can be associated with economic policies. The wavelet methodology finds a balance between time and frequency domains. Our study finds that growth Granger causes inflation at all frequency scales, starting from the short run to the very long run. Inflation, on the other hand, Granger causes growth in the long run but not in the short run. This result has implications for Bangladesh, and as such for similar developing countries, where some policymakers believe that inflation must be kept at very low levels for sustained economic growth.