Let \(f(z)=h(z)+\overline{g(z)}\), where \(h(z)=z-\sum^\infty_{k=2} |a_k|z^k\), \(g(z)=\sum^\infty_{k=1}|b_k|z^k\), be a harmonic map of the unit disk \(D\). A function \(f\) is said to be of the class \(T_H(\alpha, \beta)\), \(\alpha\geq 0\), \(\beta\)-complex number, if \(h\) and \(g\) satisfy in \(D\) the condition \[ {\mathcal R}\left\{\alpha zh''(z)+\frac{g(z)}{z} \right\}<1-|\beta|. \] The author gives in terms of coefficients of \(h\), and \(g\) a necessary condition for \(f\) to be in \(T_H(\alpha,\beta)\) and solves various extremal problems within the class. Justifications are fairly routine.