"No exact match was found...." error

I recentlyswitched move my SPS2007 to SPS2010. Old and New SPS was on different domains (old=firmblue.local, new=firmred.local).
Siteworks fine but people pickerdoes not work.
If I type a user name or any other information in people picker searchI get an error "no exactmatch...". After that, Iclick on the red underlined text andc choose exact user(although only one user is withthat name in a domain), and whenI gave him permission (eg. Read)and click OK. AgainI getthe same error "no exact..."
The error does not occur only if I type a domain username thenchoose permission and click OK.So, without peoplepicker.
This solution does not satisfy me, becausethe user who wants to give perrmissions needs to know all the usernames on the domain.