The author presents a special method of constructing of almost periodic sequences and functions attaining values in a metric space. Using this construction, it is shown, among others, that for any countable totally bounded set \(X\) in a metric space there exists an almost periodic sequence \(\{\psi _k\}_{k\in \mathbb {Z}}\) such that \(X=\{\psi _k,\, k\in \mathbb {Z}\}\) and \(\psi _k\) satisfies \(\psi _k=\psi _k+lq(k)\) for all \(k\) and some \(q(k)\) which depends on \(k\).