  Integer solutions of the diophantine equation $A^4+hB^4=C^4+hD^4$ are known
for all positive integer values of $h < 1000$. While a solution of the
aforementioned diophantine equation for any arbitrary positive integer value of
$h$ is not known, Gerardin and Piezas found solutions of this equation when $h$
is given by polynomials of degrees 5 and 2 respectively. In this paper, we
present several new solutions of this equation when $h$ is given by polynomials
of degrees $2,\;3$ and 4.
