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Let $A$ be an associative simple (central) superalgebra over ${\mathbb C}$and $L$ an invariant linear functional on it (trace). Let $a\mapsto a^t$ be anantiautomorphism of $A$ such that $(a^t)^ t=(-1)^{p(a)}a$, where $p(a)$ is theparity of $a$, and let $L(a^t)=L(a)$. Then $A$ admits a nondegeneratesupersymmetric invariant bilinear form $\langle a, b\rangle=L(ab^t)$. For$A=U({\mathfrak{sl}}(2))/{\mathfrak{m}}$, where ${\mathfrak{m}}$ is any maximalideal of $U({\mathfrak{sl}}(2))$, Leites and I have constructed orthogonalbasis in $A$ whose elements turned out to be, essentially, Chebyshev (Hahn)polynomials in one discrete variable. Here I take$A=U({\mathfrak{osp}}(1|2))/{\mathfrak{m}}$ for any maximal ideal${\mathfrak{m}}$ and apply a similar procedure. As a result we obtain eitherHahn polynomials over ${\mathbb C}[\tau]$, where $\tau^2\in{\mathbb C}$, or aparticular case of Meixner polynomials, or --- when $A=\mbox{Mat}(n+1|n)$ ---dual Hahn polynomials of even degree, or their (hopefully, new) analogs of odddegree. Observe that the nondegenerate bilinear forms we consider fororthogonality are, as a rule, not sign definite

Enveloping Superalgebra U(osp(1|2)) and Orthogonal Polynomials in Discrete Indeterminate