Consider the complex matrix Lie superalgebra $gl_{ N|N}$ with the standard generators $E_{ ij}$ where $i,j=-N,...,-1,1,...,N$. Define an involutive automorphism $\eta$ of $gl_{ N|N}$ by $\eta(E_{ ij})=E_{ -i,-j}$. The queer Lie superalgebra $q_N$ is the fixed point subalgebra in $gl_{ N|N}$ relative to the automorphism $\eta$. Consider the twisted polynomial current Lie superalgebra $g=\{ X(t)\in\gl_{ N|N}[t]:\eta(X(t))=X(-t)\}$. The enveloping algebra $U(g)$ of the Lie superalgebra $g$ has a deformation, called the Yangian of $q_N$. For each $M=1,2,...$ denote by $A_N^M$ the centralizer of $q_M\subset q_{ N+M}$ in the superalgebra $U(q_{ N+M})$. We describe the projective limit of the sequence of centralizer algebras $A_N^1,A_N^2,...$ in terms of the Yangian of $q_N$.
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