Lock and read next

Is there a way if one transaction has locked a row in a table, the next transaction does not get blocked while reading the same row, but moves on to the next record in the table to read?

Example:

Transaction 1

Select * from table LIMIT 1 FOR UPDATE

--transaction takes 3 min to complete

Transaction 2

Select * from table LIMIT 1 FOR UPDATE

Here, transaction 2 blocks on the same record that transaction 1 has a write lock on (for 3 min). Is there a way to tell transaction 2 to move on and get the next writable record?

Thanks,

Girish