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In this paper, we concisely represent the general solution for the TM$_{1,2}$mixing in the type-I minimal seesaw mechanism and show phenomenologicalconstraints of the Yukawa matrix of neutrinos $Y$. First, conditions of $Z_{2}$symmetry associated with TM$_{1,2}$ restrict two complex parameters. Inaddition, three complex parameters are constrained from five phenomenologicalparameters (two neutrino masses $m_{i}$, the mixing angle $\theta_{13}$, theDirac phase $\delta$, and the Majorana phase $\alpha$) and the overall phase.As a result, there is only one free complex parameter for $Y$, except for theright-handed neutrino masses $M_{1,2}$.  For the TM$_{1}$ mixing with normal hierarchy, the symmetry condition isimposed only on $Y$, and the physical parameters depend on $M_{R}$. In othersituations, the dimensionless parameters $(\theta_{13}, \delta$ and $\alpha)$do not depend on $M_{R}$ but only on certain combinations of the components of$Y$.

General solutions for TM$_{1,2}$ mixing in the minimal type-I seesaw mechanism and phenomenological constraints to Yukawa matrix of neutrinos