Cannot login to subsites

I’ve just installed my WordPress 3.4.1 and setuped my multisite network, but I failed to login to my second site.

How I setuped the network:
Generally I followed the instructions document Create A Network and created a domain-based network. I chose to use two independent first-level domains for the two sites. Both of the sites were accessible after the setup of the network.

What problems I met:
When I was logined as the super user, I made attempt to move from the dashboard of my primary site to that of the subsite. However, the Login page appears and asked me to login again. So I tried logining as either the super user or the admin of the subsite, but both resulted in returning to the Login Page. Meanwhile I can login to the dashboard of the network or the primary site.

What I have tried:
I first checked if I have got the wrong password, so I purposely input a wrong password, and that gives the incorrect password warning, which means the loop mentioned above was not brought by a mistaken password.
Then I recalled that it was a wide-spread problem four years ago when users upgrades WP 2.5 to WP 2.6 so that I began to search for solutions posted then. I’ve tried several of following so-called working solutions, but none of them works:
Modifying the cookie configuration in wp-includes/pluggable.php
Clear up the cache/cookies of my broswer
Checking the siteurl and home value in wp_options of the database
Checking the character codes in the database
Disable all the plugins

Looking forward to further solutions. Thanks a lot.