Cannot use Linked Server unless I have sysadmin role

I have a local SQL Server 2008R2.  I have configured Linked Server to a remote database. 

The Linked Server works great when I login to the local server using a SQL-login account withsysadmin server role.  I can query against the remote server, so I know the Linked Server setting is correct.  However, I would get the error below if I use an account that does not have thesysadmin server role.

Msg 7416, Level 16, State 2, Line 2
Access to the remote server is denied because no login-mapping exists.

For both local and remote servers, SQL login is used (Windows authentication is not used)

What kind of security I need to configure for a regular SQL-login account to use Linked Server?