1. Since it is already in the terms of your present employment agreement that you shall have to give one month's notice or forego one month's salary in lieu thereof, you can quit your present job by submitting your resignation asking your employer to deduct one month's basic pay from your dues. If there is no due then you can attach a cheque for that amount,
2. You can thereafter join your new Company,
3. It is not good to supress vital information from employers since such suppression may create problem later on,
4. However, since you have no other option left before you, you sahll have to join the new company as a fresh candidate and in the said event you won't be able to record your 4 months experience with your present Company in your CV.