Using first-principles calculations, we identify a new orthorhombic boron nitride (BN) phase (namely, P-BN; space group: Pmn2(1)), which has similar topological structure to Bct-BN and Z-BN, but without the six-membered ring. This P-BN allotrope is energetically more favorable than previously reported Pnma-BN, Bct-BN and Z-BN phases. With only 0.06 eV/atom less stable than h-BN at ambient pressure, it can be formed from h-BN under cold compression at a low pressure of 4 GPa. The theoretical hardness and bulk modulus of the P-BN crystal are 403 GPa and 60.5 GPa, respectively, comparable to those of c-BN. Moreover, the P-BN phase along with Bct-BN and Z-BN are suggested as possible intermediate phases between h-BN and w-BN, which can be qualitatively explained by two empirical rules of Ostwald and Ostwald-Volmer.