To investigate the impact of new physics effects on P + → ℓ $^{+}$ν , in this paper, we concen- trate on the charged Higgs mediated effects in the two-Higgs-doublet model (THDM) [20]. It is well known that the general THDM leads to flavor changing neutral currents (FCNCs) at the tree level. For avoiding the large tree level FCNCs, some discrete or global U (1) sym- metry has to be imposed so that one Higgs doublet couples to up-type quarks while another one couples to down-type quarks [21], where now it is named by type-II THDM. Although in large tan β scenario (definition given below), the charged Higgs has an important impact on the P + → ℓ $^{+}$ν , however its contributions are destructive and make the theoretical results further depart from experiments [5, 22]. In addition, the nonuniversal lepton couplings in R$_{K}$ are eliminated, i.e. the value of R$_{K}$ in type-II THDM is the same as that in the SM [1]. Hence, in order to enhance f$_{D}$$_{s}$ and B ( B + → τ $^{+}$ν ) and show the violation of lepton univer- sality in R$_{K}$ , our purpose is to explore the intriguing scenario for Yukawa matrices which could lead to free of FCNCs at the tree level in the THDM without imposing symmetry. We start with writing the Yukawa sector in THDM as with ˜ H$_{k}$ = iτ$_{2}$H ∗ $_{k}$. We can recombine H$_{1}$ and H$_{2}$ so that only one of Higgs doublets develops vacuum expectation value (VEV). Accordingly, the new doublets are expressed by where sin β = v$_{1}$/v , cos β = v$_{2}$/v , v = √ v 2 1 + v 2 $_{2}$, < H > = 0 and < h > = $_{v/}$√$_{2. As a result,}$ Eq. (4) can be rewritten by − L Y = ¯ Q$_{L}$Y U 1 U$_{R}$ ˜ H$_{1}$ + ¯ Q$_{L}$Y U 2 U$_{R}$ ˜ H$_{2}$ + ¯ Q$_{L}$Y D 1 D$_{R}$H$_{1}$ + ¯ Q$_{L}$Y D 2 D$_{R}$H$_{2}$ + h.c. (4) h = sin βH$_{1}$ + cos βH$_{2}$ =   G + ( v + h 0 + iG $^{0}$) $_{$_{/}$√$_{2}$}$  , H = cos βH$_{1}$ − sin βH$_{2}$ =   H + H 0 + iA 0   (5) − L Y = ¯ Q$_{L}$ ¯ Y U 1 U$_{R}$ ˜ h + ¯ Q$_{L}$ ¯ Y U 2 U$_{R}$ ˜ H + ¯ Q$_{L}$ ¯ Y D 2 D$_{R}$h − ¯ Q$_{L}$ ¯ Y D 1 D$_{R}$H (6) 3