IPV4 TTL

hi,
In ipv4 there is a ttl field which changes at every router till
it reaches the destination from the source.
We have a header check sum in ipv4 header which is calculated at
the time of transmission of packet from source .
If this TTL field changes then Do we need to change the header
check sum where every the TTL changes . Who does this change if it is
done ?
If it is not done doesnt the receive drop the packet since TTL has
changed and CRC is different....

Regards,
uday