Sql-server – database mirror problem with Network Service account

I have two SQL Server 2008 R2 instances installed on same Server and the engine log on as Network Service account which is set by installation.

there is a database TestDB on both instances. I try to setup database mirror for this case and I failed with following error:

The server network address "TCP://myserver.mycompany.com:5023" can not be reached or does not exist. Check the network address name and that the ports for the local and remote endpoints are operational. (Microsoft SQL Server, Error: 1418)

Then I changed the account to Local System for engine and restarted sql server service and I am able to setup mirror.

How to resolve this problem if I want to keep Network Service to run the engine service?