Should I split my deposits across different banks?

I've come into a large sum of money and am planning to open a 6-month time deposit. I have already placed 500 million KRW in IBK (Industrial Bank of Korea) and am looking to add another 400 million KRW. There is no need to use a different bank, right?
Since IBK is my main bank,
I am planning to deposit the additional amount there as well.