Can I transfer H1B which was valid till 2006 or I need to go for new H1-B?

For past 3 years I am in USA on L1 Visa with the current company. Earlier I had traveled to USA on H1-B. The old H1B was valid till 2006. In case I am looking for a job change can I transfer the old H1-B? In that case I don’t have to apply for a new H1-B. Any response on this query will be greatly appreciated.

Your old H-1 was more than 6 years ago. I don’t think you can use it for cap-exempt petition now. You should have it filed in the next cap.