Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
We cannot give a judgement on Faisal Islamic Bank because we do not know the reality of its transactions.
If it is proven for sure that this bank invests its money in other banks which deal with interest and usury, then it is not permissible to deal with this bank or to deposit money in it except for a necessity.
However, if the bank is only opening current accounts without any usury or interest in other banks for the necessity of money transactions, then there is no harm according to many scholars. But other transactions of the bank have to be considered as well; if they are according to Islamic principles, then it is acceptable to deal with it, otherwise not.
Allah knows best.