In thispaper,we introduceanewhomological notionrelated tobiprojectiveBanachalgebras,namely-biprojectiveBanachalgebras.Westudytherelationbetweenthisnew notionandtheotherhomologicalnotions,such asamenability, pseudo-amenabilityandinner amenability.Also,weinvestigatethisnewnotiononcertainBanachalgebrassuchasgroup algebras,LipschitzalgebrasandtriangularBanachalgebras.