\textit{G. Navarro} [J. Aust. Math. Soc., Ser. A 61, No. 3, 369-376 (1996; Zbl 0874.20006)], introduced the good bases. If \(G\) be a finite group, \(H\subseteq G\) and \(\text{cf}(H)^G=\{\alpha^G\mid\alpha\in\text{cf}(H)\}\), then a basis \(B\) of this subspace is good if it satisfies the following two conditions: (I) If \(\eta\in B\), then there is \(\alpha\in\text{Irr}(H)\) such that \(\alpha^G=\eta\). (D) If \(\gamma\in\text{Irr}(H)\), then \(\gamma^G=\sum_{\eta\in B}a_\eta\eta\), where \(a_\eta\) are nonnegative integers. In general, there do not exist good bases, but if there exists one, then it is easy to show that it is unique. The good basis is denoted by \(P(G|H)\), the unique good basis of \(\text{cf}(H)^G\) (if it exists). Suppose that \(P(G|H)\) exists. One of the main features of the good bases is that they allow us to define, via this good basis, a canonical partition of \(\text{Irr}(G)\). Two characters \(\chi,\psi\in\text{Irr}(G)\) are \(H\)-linked if and only if there is \(\eta\in P(G|H)\) such that \([\chi,\eta]\neq 0\neq[\psi,\eta]\). The \(H\)-blocks of \(G\) are the connected components of \(\text{Irr}(G)\) induced by this linking (the \(H\)-blocks depend only on the conjugacy class of \(H\)). Some examples of known good bases are the following. If \(H\triangleleft G\), then \(P(G|H)\) exists. If \(\Theta\) is a complete set of representatives of the orbits of the action of \(G\) on \(\text{Irr}(H)\) then \(P(G|H)=\{\theta^G\mid\theta\in\Theta\}\) and the \(H\)-blocks are \(\text{Irr}(G|\theta)\) for all \(\theta\in\Theta\). Suppose that \(G\) is a \(p\)-solvable group and \(H\) is a \(p\)-complement of \(G\). Then by Fong's theory we have that \(P(G|H)=\{\Phi_\varphi\mid\varphi\in\text{IBr}(G)\}\) exists, where the \(\Phi_\varphi\) are the indecomposable projective characters of \(G\) and the \(H\)-blocks are the Brauer \(p\)-blocks. Let \(G\) be a \(\pi\)-separable group and let \(H\) be a Hall \(\pi\)-subgroup of \(G\). Then \(P(G|H)\) exists, and the \(H\)-blocks are the \(\pi\)-blocks of Isaacs-Slattery. In particular \(P(G|H)\) exists, if \(H=P\in\text{Syl}_p(G)\) and \(G\) is \(p\)-solvable. If \(G\) is a solvable group and \(H\) is a nilpotent injector, then \textit{G. Navarro} [loc. cit.] proved that \(P(G|H)\) exists. In this paper the authors determine the \(H\)-blocks which they denote \(N\)-blocks. There exists a well-behavior of the theory of \(N\)-blocks. This is similar to Fong's theory of \(p\)-blocks of \(p\)-solvable groups, in which the \(p'\)-radical \(O_{p'}(G)\) is replaced by the Fitting subgroup \(F(G)\) and the \(p\)-complements of \(G\) by nilpotent injectors of \(G\). In this paper, they show that \(N\)-blocks of \(G\) are described inductively by a Fong-Reynolds theorem and a theorem of Fong type. The correspondence to the \(k(B)\)-conjecture of R. Brauer is satisfied by the \(N\)-blocks. That is, if \(G\) is a solvable group, \(B\) is an \(N\)-block of \(G\) and \(H\) is a nilpotent injector of \(G\), then \(|B|\leq|G:H|\). The key to prove the above result is that \(k(G/F(G))\leq|G:I|\) where \(G\) is a solvable group and \(I\) is a nilpotent injector of \(G\) proved by \textit{M. J. Iranzo}, \textit{G. Navarro} and \textit{F. Pérez Monasor} [Isr. J. Math. 93, 185-188 (1996; Zbl 0852.20010)]. They also show the fact that the nilpotent injector size and the union of its conjugates are determined by the character table.