  A $(G,[k_1,\dots,k_t],\lambda)$ {\it partitioned difference family} (PDF) is
a partition $\cal B$ of an additive group $G$ into sets ({\it blocks}) of sizes
$k_1$, \dots, $k_t$, such that the list of differences of ${\cal B}$ covers
exactly $\lambda$ times every non-zero element of $G$. It is called {\it
Hadamard} (HPDF) if the order of $G$ is $2\lambda$. The study of HPDFs is
motivated by the fact that each of them gives rise, recursively, to infinitely
many other PDFs. Apart from the {\it elementary} HPDFs consisting of a Hadamard
difference set and its complement, only one HPDF was known. In this article we
present three new examples in several groups and we start a general
investigation on the possible existence of HPDFs with assigned parameters by
means of simple arguments.
