  A new method of composition orthogonality is introduced. It is applied to
generate new sequences of orthogonal polynomials and functions. In particular,
classical orthogonal polynomials are interpreted in the sense of composition
orthogonality. Finally, new sequences of orthogonal polynomials with respect to
the weight function $x^\alpha \rho^2_\nu(x), \rho_{\nu}(x)= 2 x^{\nu/2}
K_\nu(2\sqrt x),\ x >0, \nu \ge 0, \alpha > -1$, where $K_\nu(z)$ is the
modified Bessel function or Macdonald function, are investigated. Differential
properties, recurrence relations, explicit representations, generating
functions and Rodrigues-type formulae are obtained. The corresponding multiple
orthogonal polynomials are exhibited.
