Trigger AFTER UPDATE OR INSERT

Hello frnds,
I have a trigger on a table with After UPDATE OR INSERT ..that insert
a record in an another table..........If the Trigger Fire Correctly
the row is inserted or updated in the database as the case is. But if
it is not fire correctly then the table is also not updated on which
the trigger is..............

Is it the right .................? if yes......How to insert the
record in the table if the trigger is failed.

Regards, Yogesh Arora.