SMTP settings for sending mail OUTSIDE the domain

I am using the following code which I modified from the knowledge base:
Dim strFrom =postmaster account

Dim MailMsg As New MailMessage(New MailAddress(strFrom.Trim()), New MailAddress(address))
MailMsg.BodyEncoding = Encoding.Default
MailMsg.Subject = thesubject
MailMsg.Body = mailmessage

MailMsg.IsBodyHtml = True
'Smtpclient to send the mail message

Dim SmtpMail As New SmtpClient
Dim basicAuthenticationInfo As New System.Net.NetworkCredential("thepostmasteraccount", "thepassword")--obviously these are the correct account and password

SmtpMail.Host = the correct smtp host
SmtpMail.UseDefaultCredentials = False
SmtpMail.Credentials = basicAuthenticationInfo

SmtpMail.Send(MailMsg)

However, I am getting an error when sending the email. The error is Mailbox unavailable: no such user here. I realize this is because I am sending OUTSIDE my domain. But how do I get this to send outside the domain?