The home, on Ferrybridge Road, was first rated inadequate having been inspected in February 2021 by the Care Quality Commission (CQC).
Following a further inspection in April this year, the CQC has now given the home an overall rating of 'requires improvement'.
The service managers, the Waash Group, said the new rating represents months of hard work by a new management team which is determined to continue to improves services for residents.
The Beeches provides accommodation and nursing care for up to 23 people aged 65 and over, some of whom are living with dementia.
At the time of the latest inspection 20 people were living at the home.
The CQC report states: "People said they felt safe and happy living at The Beeches.
"They said the food was good and they liked the staff.
"The provider had improved the management of people's medicines.
"We saw improvement in the assessment, recording and management of risks related to people's health and the environment.
"Although, there was a need to continue to develop people's risk assessments."
The report states the provider had made improvements to "oversight and governance arrangements".
The audit systems were found to be effective in highlighting and addressing shortfalls and concerns.
Improvements spanned medicines management, care planning, record keeping and fire safety.
The report also states: "The provider had made improvements to the home environment.
"This included refurbishing and replacing bathrooms and toilets, making improvements to the garden.
"Signage and decoration had been improved to support the needs of people living with dementia.
"People were supported to have maximum choice and control of their lives and staff supported them in the least restrictive way possible and in their best interests."
The report concludes: "This service has been in Special Measures since April 14, 2021.
"During this inspection the provider demonstrated that improvements have been made.
"The service is no longer rated as inadequate overall or in any of the key questions. Therefore, this service is no longer in Special Measures."
A spokesman for Waash Group said: "Everything at this home now revolves around our residents.
"We will move heaven and earth to provide the services anyone would want their loved ones to have.
"The journey does not stop here.
"We will continue to ensure that our residents and their families continue to be happy with the services we provide.
"It is due to the hard work of everyone at the home that we have reached this stage and we expect our ratings to continue to improve."