  Fixed points ${\bf u}=\varphi({\bf u})$ of marked and primitive morphisms
$\varphi$ over arbitrary alphabet are considered. We show that if ${\bf u}$ is
palindromic, i.e., its language contains infinitely many palindromes, then some
power of $\varphi$ has a conjugate in class ${\mathcal P}$. This class was
introduced by Hof, Knill, Simon (1995) in order to study palindromic morphic
words. Our definitions of marked and well-marked morphisms are more general
than the ones previously used by Frid (1999) or Tan (2007). As any morphism
with aperiodic fixed point over binary alphabet is marked, our result
generalizes the result of Tan. Labb\'e (2014) demonstrated that already on a
ternary alphabet the property of morphisms to be marked is important for the
validity of our theorem. The main tool used in our proof is the description of
bispecial factors in fixed points of morphisms provided by Klouda (2012).
