A morphotropic phase boundary driven by epitaxial strain has been observed in a lead-free multiferroic BiFeO3 thin films and the strain-driven phase transitions were widely reported to be iso-symmetric Cc-Cc ones by recent works. In this paper, we suggest that the tetragonal-like BiFeO3 phase identified in epitaxial films on (001) LaAlO3 single crystal substrates is monoclinic MC. This MC phase is different from MA type monoclinic phase reported in BiFeO3 films grown on low mismatch substrates, such as SrTiO3. This is confirmed not only by synchrotron x-ray studies but also by piezoresponse force microscopy measurements. The polarization vectors of the tetragonal-like phase lie in the (100) plane, not the (110) plane as previously reported. A phenomenological analysis was proposed to explain the formation of MC Phase. Such a low symmetry MC phase, with its linkage to MA phase and the multiphase coexistence open an avenue for large piezoelectric response in BiFeO3 films and shed light on a complete understanding towards possible polarization rotation paths and enhanced multiferroicity in BiFeO3 films mediated by epitaxial strain. This work may also aid the understanding of developing new lead-free strain-driven morphotropic phase boundary in other ferroic systems. Comment: 22 pages,Submitted to Advanced Functional Materials on Sep,7,2010, accepted on Oct,27,2010