For a family of domains Ω_t ⊂ ℂⁿ, t ∈ [0, 1], a formula for B₁(z, s) - B₀(z, s) is established, where B₀ and B₁ are the Bergman kernels for Ω₀ and Ω₁. As an application of this formula, we obtain two terms in the asymptotics of B(z, z) as z → ∂Ω for a special class of domains.