Visa Debit Card - Online Usage?

I currently have a Visa Debit Card from Faysal Bank.. It works fine on POS transactions.. However i cant use it online to buy anything.

I wanted to open an account in another bank for only this purpose (Online Shopping). Is there any bank which provides an ATM Debit Card which works online on the internet? I cant have a credit card as im not employed. So which bank's Debit card works online? Standard Chartered? Bank Alfalah?

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