The new MySQL version shows that the client version is too low

How to solve the problem of installing client does not support Authentication Protocol requested in mysql4

After upgrading the MySQL database today, the following error occurs:
Client does not support Authentication Protocol requested by server; consider upgrading MYSQL client

Upgrade to version 4.1.7:
[Root @ eygle gbook] # mysql-uroot-p-heygle
Enter password:
Welcome to the MySQL monitor. commands end with; or/g.
Your MySQL connection ID is 44 to server version: 4.1.7-max

Type 'help; 'or'/H' for help. type'/C' to clear the buffer.

Mysql>

I found a solution on the official website:
Http://dev.mysql.com/doc/mysql/en/Old_client.html

There are two solutions:

I:
Mysql> set password
-> 'Some _ user' @ 'some _ host' = old_password ('newpwd ');

II:
Mysql> Update mysql. User SET Password = old_password ('newpwd ')
-> Where host = 'some _ host' and user = 'some _ user ';
Mysql> flush privileges;