We dramatically improved the critical current density, Jc, in applied magnetic fields, B, of MgB2 tapes fabricated via an ex situ powder-in-tube (PIT) process using an Fe sheath and MgB2 powder prepared in lab. The starting powder for this technique was obtained from the core of an MgB2 tape prepared via an in situ PIT process using a mixture of MgH2 and amorphous boron. The highest Jc at 10 T was 6.1×103 A/cm2. This value exceeds not only that of conventional ex situ MgB2 tapes made from commercial MgB2 powder but also that of in situ MgB2 tapes fabricated using MgH2(3.4×103 A/cm2). These experimental data indicate that ex situ MgB2 tapes have great potential to upgrade the Jc-B property if the quality of the starting powder is improved.