If you have configured the exchange server to use the Windows Authentication and a prompt stating to close the browser to terminate the browser session is displayed then you can switch to the Form-based authentication.
Run the following command in the Exchange Management shell to use Form-based authentication:
Set-OwaVirtualDirectory -FormsAuthentication $true -WindowsAuthentication $fasle -Identity "IDENTITY_NAME"
Replace the IDENTITY_NAME with valid hostname\owa (web site name)