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This housing market matching model considers two types of home seekers: people who search for a house both in the rental and in the homeownership market, and people who only search in the homeownership market. The house-search process leads to several types of matching and in turn this implies different prices of equilibrium. Also, the house-search process connects the rental market with the homeownership market. This model is thus able to explain both the relationship between the rental price and the selling price and the price dispersion which exists in the housing market. Furthermore, this theoretical model can be used to study the impact of taxation in the two markets. Precisely, it is straightforward to show the effects of two different taxes: the tax on property sale and the tax on rental income.