During magnetic reconnection, a "neutral sheet" current is induced, heating the plasma. The resultant plasma thermal pressure forms a stationary equilibrium with the opposing magnetic fields. The reconnection layer profile holds significant clues about the physical mechanisms which control reconnection. In the Magnetic Reconnection Experiment [M. Yamada et al., Phys. Plasmas 4, 1936 (1997)], a quasi steady-state and axisymmetric neutral sheet profile has been measured precisely using a magnetic probe array with spatial resolution equal to one quarter of the ion gyro-radius. It was found that the reconnecting field profile fits well with a Harris-type profile [E. G. Harris, Il Nuovo Cimento 23 , 115 (1962)], B(x)~tanh( x/delta). This agreement is remarkable since the Harris theory does not take into account reconnection and associated electric fields and dissipation. An explanation for this agreement is presented. The sheet thickness delta is found to be ~0.4 times the ion skin depth, which agrees with a generalized Harris theory incorporating nonisothermal electron and ion temperatures and finite electric field. The detailed study of additional local features of the reconnection region is also presented.