A new method for identifying bull and bear financial market regimes is proposed, related to a classic algorithm for picking turning points in the business cycle. Our approach uses only a single discrete parameter, adjusted to the periodicity of the data, which largely removes subjectivity from the regime identification process. Applying it to the benchmark Dow Jones Industrial Average index data, we show the method's capability of obtaining a classification similar to competing multi-parameter methods, without imposing any conditions on regime duration or amplitude. Despite its relative simplicity, our algorithm can be easily applied across different asset classes, where its direct competitors may fail, as we show in an out-of-sample identification example involving other stock indices, exchange rates and commodities. Our new market regime classification rule constitutes a relatively straightforward, but important methodological development that can be used in a broad palette of financial market research problems, where discerning different regimes is beneficial.