Immobilized single horseradish peroxidase enzymes were observed by confocal fluorescence spectroscopy during catalysis of the oxidation reaction of the nonfluorescent dihydrorhodamine 6G substrate into the highly fluorescent product rhodamine 6G. By extracting only the non-Markovian behavior of the spectroscopic two-state process of enzyme-product complex formation and release, memory landscapes were generated for single-enzyme molecules. The memory landscapes can be used to discriminate between different origins of stretched exponential kinetics that are found in the first-order correlation analysis. Memory landscapes of single-enzyme data shows oscillations that are expected in a single-enzyme system that possesses a set of transient states. Alternative origins of the oscillations may not, however, be ruled out. The data and analysis indicate that substrate interaction with the enzyme selects a set of conformational substates for which the enzyme is active.