A conformational triangle method is presented to analyze the secondary structure contents of 1028 structurally known proteins in the non-redundant data set of the recent 25% PDB_SELECT. The secondary structure contents of each protein are mapped on to a point in the triangle. It was found that the distribution of the 1028 points is strongly skewed in the triangle and about 42% of the whole area is empty, which is called the forbidden area. The detailed border between the allowable and forbidden areas was calculated. The possible explanation of the skewed distribution is discussed. The distributions of the mapping points for enzymes and non-enzymes in this non-redundant data set are compared. It was found that a necessary rather than a sufficient condition for an enzyme molecule is that its coil content must be >/=0.223. It is hoped that the skewed distribution observed here could be used to test the secondary structure and threading predictions.