"I have a clorine system to remove most of bad stuff in the water and I use a Culligan Mark 88 to remove the stain in the water. "
What kind of "chlorine system"; how is it added and how is it controlled?
From your reference to "stain", I suspect that you may have iron in your water. The chlorine will cause iron to precipitate to very fine particles and collect in the water softener. After you get enough iron in the softener it gets through the filter (Which is what I think the Culligan Mark 88 is) and you notice it. One ad that I found for "Culligan 88" cartridges was selling 50 micron cartridges, which are pretty good for removing sand but not much else. One of the ads said they are "carbon paper" cartridges, which is probably supposed to remove the chlorine.
I could be totally wrong on the Culligan 88. Tell us what it is and if it is a filter, how many, what size, and what kind/micron are the cartridges.
Regenerating the softener results in removing some of the iron from the resin bed, even if it doesn't really need regenerating. You see a reduction in staining because the iron has been removed from the softener. In the meantime, you are probably using more salt than you need to. The evidence of hardness in the water is that it is hard to make soap suds. Oversoftening can make it hard to remove the soap from your hands, and your hands seem to feel a little slippery. Try using those criteria for regenerating.
If you are getting iron stain out of the faucet, then the filter is not effective because the stain you see is really small particles of oxidized iron. Filters are supposed to remove particles. Look at your filter cartridge (if that is what the Culligan 88 is) and see what is collected on it.
You might test the theory by putting in the best available pleated or string-wound cartridge and see if it gets plugged up. Try to find something 5, 3, or 1 micron. Don't try the expensive ceramic or membrane cartridge that costs a lot of $ because it will get plugged quickly.
The "whole house" filters in most houses are too small. The Culligan 88 that I saw is sold as an "RV filter". I would put in nothing less than a 20" Big Blue size, or two of the 20" long standard diameter housings, and get 1 micron or 3 micron cartridges of a reputable brand. You probably have to order them. The following is an example of what is available and others probably have a similar product.
www.harmsco.com/pdf/IP_CalypsoBlue_FINAL_040904.pdf
More cartridges actually result in lower cartridge replacement cost because the lower flow per cartridge lets them collect more sediment before the pressure drop increases to point where they must be changed. I will leave the mathematics as an exercise for the readers.