Sorting name and score from two columns to another two columns in order by score

So in column A I have a name and in column B I have a score. In column C I would like a name and in column D I would like the score but the data needs to be sorted from High score to low score in column C and D with the appropriate name corresponding with the appropriate score.

I currently have the following formula that does part of the job.

=INDEX(A$1:A$400,MATCH(LARGE($B$1:$B$400,ROWS($1:1)),$B$1:$B$400,0)) in column C
=INDEX(B$1:B$400,MATCH(LARGE($B$1:$B$400,ROWS($1:1)),$B$1:$B$400,0)) in column D

This works unless there is a duplicate score. Then the formula returns the correct score but the name is returned for the first person who recieved that score. Any ideas on how to make the function return the unique name for duplicate scores?

Thanks in advance

Alright glenn we are close! however my lists will be around 300 entries I tried to change the numbers in the formula to reflect this and it did not work? Thank you so much for your help

=INDEX($A:$A,SMALL(INDEX(($B$2:$B$300<>D2)*300^300+ROW(B$2:B$300),0),COUNTIF(D$2:D2,D2)))

anywhere you see 300 I changed 10 to 300.

You are correct! That was silly of me. fixed and functional. Thank you for your time and I will update to resolved