Let \(h(d)\) denote the class number (in the narrow sense) of indefinite binary quadratic forms of discriminant \(d>0\) (\(d\equiv 0\) or \(1\bmod 4\), \(d\) not a square). The growth of \(h(d)\) for \(d\to \infty\) is well known to be quite erratic due to the irregular growth behaviour of the fundamental unit \(\varepsilon(d)\) of the corresponding real quadratic field. In consequence of this the growth of \(\sum_{d\leq X} h(d)\) for \(X\to \infty\) is hard to estimate. However, a different mode of enumeration of the \(h(d)\) according to the size of \(\varepsilon(d)\) leads to the sum \(\sum_{\varepsilon(d)\leq X}h(d)\) whose asymptotic behaviour can be determined by means of the Selberg zeta-function since this sum is closely related with the distribution of norms of primitive hyperbolic elements of \(SL_2(\mathbb{Z})\). The author introduces an additional summation condition and proves: There exists an absolute constant \(C>0\) such that \[ \sum_{\substack{ \varepsilon(d)\leq X\\ h(d)< C\sqrt{d}/ \log^2d }} h(d)= O(X\log^3 X) \quad\text{for}\quad X\to \infty. \]