I found this website which has some great ideas...I have experience with other caged birds, but not parakeets. hope it helps... http://www.lisashea.com/petinfo/handtrain/biting.html

Won't happen in a week. Won't happen in a month either. When you actually start to work WITH the bird, instead of trying to impose your will on it, you'll start getting somewhere. I imagine the first mistake you're making is trying to grab it from inside it's cage. Guess what, you'll get bit. How would you feel if some large monster invaded your safe spot, grabbed you and took you away from safety? If this bird is new to you and it's surroundings, give it at least a month to get used to all the comings and goings in the house. You should have it in an area that people are in frequently, but NOT in the kitchen. The non stick coatings on cookware when it's heated can kill a bird quite quickly. The fumes are bad for them. When your bird has settled in, now you can get to work. It'll want to bite you at first. That's normal. The trick is to simply not use your fingers for getting it to step up. Use a short wooden perch. Place it gently under it's chest and gently push back against it. The bird will have to get on the perch you are holding or it will fall. Say "step up" when you are doing this. If the bird is a talker (not all are), eventually, that will likely be the first thing it says to you, especially when it wants up. Mine asks to be picked up this way or will step up when I ask him to. The same goes for letting the bird down with the perch you are holding. Say "step down" and with him on the hand held perch, push it's chest, just above the legs, into the bird cage perch. Give it a treat for all of this. If your bird has it's wings clipped, you can actually do all this from the top of the cage. Your bird won't be able to go far but make sure doors and windows are shut and anything that may injure it, are out of the room. Do this a couple of times a day. After a week shorten the distance between your hand and the end of the perch you hold. This will get the bird used to your hand being closer. When you're down to just a couple of inches between your hand and the bird, you're ready to try using your finger. It's make or break time now. If the bird bites, say "No", sternly, push back against the bite gently but firmly. This causes the bird to start to lose it's balance. It has a choice to make, fall or stop biting. I guarantee that it will stop the bite. Keep on trying for 10 minutes. If it steps up, with no bite, reward it with it's favorite treat. The important thing to remember at the end here, is that you make no sudden movements, be consistent, reward when it deserves a reward, NEVER hit it not even a tap on the beak and don't manhandle the bird. Even the nastiest bird that has never had any human contact will eventually come around and not bite you all the time. The same goes for a hand raised bird. They will bite when they are in a bad mood, bored or you do something unexpected. Don't think for a minute that it will never bite again. It will. The trick is to get to know your bird and it's body language. If this bird was hand raised, then you should be done this basic training in a month - a month and a half. If the bird was never handled at all in the store you bought it from, then it can take upwards of 6 months.

Pull its teeth? ----------- But seriously folks. For one thing if it is biting that means it is upset with the situation, it is either afraid or angry. Now I don't know about you, personally I don't poke a bear if I think it will not like or or worse if poking the bear will make it angry. Granted there are a few minor differences between a bird in a cage and a bear in the woods but the same thing applies not so much because a bear will maul you and the bird can't, but because the treatment of either is plain wrong. Most likely you need to spend time with the bird, in the cage with you right there talking to it, and making movements which are NOT threatening and slowly work toward handling it. I had a parrot who was badly abused and it took months of slowly approaching her to get her used to my presence. She spent the majority of the rest of her life on my shoulder. Time, pateince and lots of love.

My parakeet does the same thing,it will make it worse if you pick him up, or petting him on the head. You should spend time with him more, and play soft music to him or whistle. Pet him softly and talk to him softly.That should help a little.