A protein secondary structure prediction method from multiply aligned homologous sequences is presented with an overall per residue three-state accuracy of 70.1%. There are two aims: to obtain high accuracy by identification of a set of concepts important for prediction followed by use of linear statistics; and to provide insight into the folding process. The important concepts in secondary structure prediction are identified as: residue conformational propensities, sequence edge effects, moments of hydrophobicity, position of insertions and deletions in aligned homologous sequence, moments of conservation, auto-correlation, residue ratios, secondary structure feedback effects, and filtering. Explicit use of edge effects, moments of conservation, and auto-correlation are new to this paper. The relative importance of the concepts used in prediction was analyzed by stepwise addition of information and examination of weights in the discrimination function. The simple and explicit structure of the prediction allows the method to be reimplemented easily. The accuracy of a prediction is predictable a priori. This permits evaluation of the utility of the prediction: 10% of the chains predicted were identified correctly as having a mean accuracy of > 80%. Existing high-accuracy prediction methods are "black-box" predictors based on complex nonlinear statistics (e.g., neural networks in PHD: Rost & Sander, 1993a). For medium- to short-length chains (> or = 90 residues and < 170 residues), the prediction method is significantly more accurate (P < 0.01) than the PHD algorithm (probably the most commonly used algorithm). In combination with the PHD, an algorithm is formed that is significantly more accurate than either method, with an estimated overall three-state accuracy of 72.4%, the highest accuracy reported for any prediction method.