I advice you to perform nested PCR or what is named duplicated PCR at which all the non-specific bands will be removed by second round PCR. Each of Taq DNA polymerase, forward and reverse primers and nucleotides will be targeted against target gene. Thus, specific bands will be appeared.
Try doing a temperature gradient. So pick one sample and use it at lower and higher annealing temperature you used. That way you can see which annealing temperature is the best.
Did you perform the temperature gradient to analyze which temperature is best? They look like non-specific bands, maybe you should raise the temperature a bit, but you need to first check which one is the right one.
Hi, in my experience I used less amount of MgCl2 and 2 degrees above (Annealing) if your amplicon size doesn't exceed 200 bp, or until 4 degrees if is bigger than that.
I would suggest to use Touchdown-PCR as Kamal Kumar already said. For this method you decrease the annealing temperature with every step of the cycle. If your calculated Tm is for example 63°C you could start e.g. at 67°C and go down e.g. 0.5°C each cycle. This reduces amplification of unspecific products since the most specific annealing temperature can be used and so the production of your product of interest starts many cycles before unspecific products are produced by unspecific primer binding (at lower temperatures).
Another idea is to cut out the band you want to have, make a gel extraction and use the product as template for the next PCR. The unspecific binding sites should not be included in the template any longer.
Many researchers have answered you to rectify the problem. But I feel that Touchdown PCR will work most and you can raise the annealing temperature by 2-3 degree.