The resistance, magnetization and strain measurements have been carried out on MnFeP0.45As0.55 compound. We found that, at variance with what is commonly believed, the critical temperature points for the first order t ransition, paramagnetism-ferromagnetism transition, and lattice anomaly are not identical. The first order transition goes on in a quite wide temperature range with a thermal hysteresis of about 10K. In the duration of the first order trans ition, the paramagnetism-ferromagnetism transition is observed, which indicates that they are not related to the lattice anomaly. Thus, we attribute it to the continuous change of the lattice parameters due to the structure transition bas ed on our observation and Zach et al.'s work. On the other hand, the lattice ano maly occurs at lower temperature than that of the first order structural and mag netic transitions. We conclude that it is a magnetostrictive behavior associate d with the magnetoelastic coupling below the Curie temperature.