Insurance Transfer for second hand car?

I have recently bought a second hand Maruti WagonR (2006). Vehicle ownership, RC etc. is been transferred. The car insurance is going to expire on 15th March'2010. As 15th march is round the corner, I am thinking to buy new car insurance from 16th March'2010. Just wondering - Is it necessary to transfer the valid insurance of a second hand car?

It is always good to have insurance in your name for dealing with any uncertainty of future claim.