Sleep spindles are significant rhythmic transients present in the sleep electroencephalogram (EEG) of non-rapid eye movement (NREM) sleep. Automatic sleep spindle detection techniques are sought for the automation of sleep staging and the detailed study of sleep spindle patterns, of possible physiological significance. A deficiency of many of the available automatic detection techniques is their reliance on the amplitude level of the recorded EEG voltage values. In the present work, an automatic sleep spindle detection system that has been previously proposed, using a Multi-Layer Perceptron (MLP) Artificial Neural Network (ANN), was evaluated using a voltage amplitude normalization procedure, with the aim of making the performance of the ANN independent of the absolute voltage level of the individual subjects' recordings. The application of the normalization procedure led to a reduction in the false positive rate (FPR) as well as in the sensitivity. When the ANN was trained on a combination of data from healthy subjects, the reduction of FPR was from 42.6% to 19%, while the sensitivity of the ANN was kept at acceptable levels, i.e., 73.4% for the normalized procedure vs 84.6% for the non-normalized procedure.