Black hair can mean many different things: wavy, curly, kinky or some combination of the three. The care of it is equally complicated and many choose to chemically relax their hair so they have the option of wearing straight and textured styles. To transition a relaxed mane of hair to a coldwave perm, grow out your relaxer first, then perm the hair.
Stop relaxing your hair. If you plan to eventually apply a coldwave perm to your hair, you will need to apply it to your natural hair, not relaxed strands. Relaxers and perms are very similar in their application and both are strong chemicals, so you cannot apply one on top of the other.
Protect your natural texture. Hair generally grows about 1/4 of an inch each month, so if you want 6 inches of natural hair before you apply the coldwave perm, for example, you'll need to grow out your hair for at least 12 months before chopping off the relaxed ends. It can be difficult styling hair with two different textures (relaxed/textured and relaxed/straight). To help with the transition, consider asking your hair stylist to style your hair into braids or twists or routinely straighten the new growth (natural hair) with heat.
Deep condition your natural hair to protect it and prep it for the impending coldwave perm. Deep condition the hair regularly, about once a week, with a product designed to infuse naturally curly or kinky hair with moisture. You'll want this hair to be strong before applying another chemical.
Chop off your relaxed ends after growing a few inches of natural hair. You may do this process yourself, since it will be evident where the line of demarcation is between your relaxed hair and natural hair. Or, you may prefer to have a professional hairstylist do this cut for you.
Choose a stylist to apply your coldwave perm. Like relaxers, coldwave perms are potent chemicals, so do not attempt them at home. The best salon referrals come from word-of-mouth, but if you don't know anyone with a perm, visit web boards to find a stylist who is versed in black hair.
Find pictures of your desired look. A perm can produce many types of curls. Flip through magazines and look for models, actresses, singers or anyone else in the pages who has a similar face shape to you and has the type of curls that you would like (tight and springy, or loose and bold, or any other type of curl pattern). Bring this picture with you when you have your appointment so that the stylist knows exactly what you expect.
Ask for moisture infusion. Perms dry out the hair and naturally textured hair is already naturally dry, so the extra moisture infusion step that some stylists perform with a perm is absolutely necessary for black hair. Your stylist should be familiar with the process, which is done before neutralizing the hair, while the hair shaft is open to receive moisture.