Do banks have right decline offers for houses with full asking price then put back on market with lower value?

My family and I are looking for houses for personal residence. We saw a bank owned house and we offered a full asking price in cash but we were told our offer was not accepted and they were in negotiation with another buyer, they said they would let us know if that offer didn't work out, we didn't hear back from bank and now 3 days later we just saw this house back on market again, $4,000 lower than what we offered. I'm wondering if this is legal in real estate market?