Is it permissible to buy a house from a non-Islamic bank, without any interest; they call it here "fixed rate"?

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.

If the matter is as you have stated that buying a house from this non-Islamic bank does not involve usury and interest, then there is no harm in that, as long as there is no breaching of the Islamic jurisprudence, like an aleatory contract, or a sale the price of which is not defined, or helping in anything that is Haram.

However, what the questioner mentioned is strange because the banks that deal with usury and interest do not give a loan except with usury and interest, and it is unlikely that they would agree to a contract in which they have no interest.

Perhaps they own the house and they sell it to you with a more expensive price than the price they bought it with, there is no harm in this but the conditions mentioned above should be observed.

However, it is better to buy through an Islamic institution, so that we do not give affluence to banks that deal with interest and usury.

Allah knows best.