Rapid progress in the stellar pulsation research has presented many new challenges to traditional pulsation theory. The following progress made by us should belong to one of the new challenges:

1. 1) There are many variable stars located at the Horizontal Branch (HB) but outside the instability strip with amplitude larger than 0.02 mag.

Maybe some astronomers have already doubted of the 1950’s conclusion-the RR Lyrae stars are confined to the narrow instability strip in the C-M diagram, the boundaries of the gap are extremely sharp and definite, beyond the edges no light variations occur with ranges greater than 0.02 mag. We are changing the conclusion by observations. Here we do not mean the microvariability. We still raise the question from the classical viewpoint. We want to show that there are variable stars outside the strip with peak to peak amplitudes larger than 0.02 mag.