I have checked that the redirection works well. I have checked that there is no link in my site that points to the old page. Is there anything else I should do?
Yes. Check again. If you have an advanced setup like myself, you can use a command line tool like curl to check a webpage and see if it returns correct data. A page with malformed headers and/or data can confuse google.
Visit this site: https://redbot.org/
Then enter a URL that is supposed to redirect to another URL. When you hit submit, you'll see the headers that are returned.
If you see the following lines:
HTTP/1.1 301 Moved Permanently
and the Location line is somewhere in the headers and "http://example.com/new" is replaced with the actual URL of your page, then you're on the right track.
Now put in the new URL and hit submit and you should see the following line at the top of the headers:
HTTP/1.1 200 OK
The only variances in the HTTP/1.1 protocol allowed is that the OK after 200 can be changed to something different, and same goes with "Moved permanently".
HTTP/2.0 might produce different results but the idea is the same. One page returns headers that instruct a browser to redirect automatically, and another page returns headers that instruct a browser that there is content on the page to display to the guest.
Just for sanity purposes, I'd recommend using apache's built-in redirection pages since the title tag of that page is different from what you would use for your pages.