Recently I did some 301 redirections on one of my websites. First I did the non www to www redirect on the .htaccess file. Then I did the list of 301 redirects from the old urls to the new ones. Redirects seems to be working properly reaching out all the way to the new url.
E.g. domain.com/page1.html--->www.domain.com/page1.html-->www.domain.com/newpage.html
Although this is part of what I set up (the non www to www redirect) I am concern for the final link not being recognize by search engines, because when I went to the 301 redirect checker it only recognized the 301 redirect from domain.com/page1.html to www.domain.com/page1.html
Should I be concern because the 301 redirect checker didn't recognize the last link, although users are getting there?